{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stats Review: The Most Dangerous Equation\n",
    "\n",
    "In his famous article of 2007, Howard Wainer writes about very dangerous equations:\n",
    "\n",
    "\"Some equations  are  dangerous  if you  know them, and others are dangerous if you do not. The first category may  pose  danger  because the secrets  within its bounds open  doors  behind which lies terrible peril. The obvious winner in this is Einstein’s ionic equation \\\\(E = MC^2\\\\), for it  provides  a  measure of  the  enormous energy hidden  within  ordinary  matter. \\[...\\] Instead I am interested in equations that unleash their danger not when we know about them, but rather when we do not. Kept close at hand, these equations allow us to understand things clearly, but their absence leaves us dangerously ignorant.\"\n",
    "\n",
    "The equation he talks about is the Moivre’s equation:\n",
    "\n",
    "$\n",
    "SE = \\dfrac{\\sigma}{\\sqrt{n}} \n",
    "$\n",
    "\n",
    "where \\\\(SE\\\\) is the standard error of the mean, \\\\(\\sigma\\\\) is the standard deviation and \\\\(n\\\\) is the sample size. Sounds like a piece of math the brave and true should master, so let's get to it.\n",
    "\n",
    "To see why not knowing this equation is very dangerous, let's take a look at some education data. I've compiled data on ENEM scores (Brazilian standardised high school scores, similar to SAT) from different schools for a period of 3 years. I also did some cleaning on the data to keep only the information relevant to us. The original data can be downloaded in the [Inep website](http://portal.inep.gov.br/web/guest/microdados#).\n",
    "\n",
    "If we look at the top performing school, something catches the eye: those schools have a fairly small number of students. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>school_id</th>\n",
       "      <th>number_of_students</th>\n",
       "      <th>avg_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>16670</th>\n",
       "      <td>2007</td>\n",
       "      <td>33062633</td>\n",
       "      <td>68</td>\n",
       "      <td>82.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16796</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065403</td>\n",
       "      <td>172</td>\n",
       "      <td>82.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16668</th>\n",
       "      <td>2005</td>\n",
       "      <td>33062633</td>\n",
       "      <td>59</td>\n",
       "      <td>81.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16794</th>\n",
       "      <td>2005</td>\n",
       "      <td>33065403</td>\n",
       "      <td>177</td>\n",
       "      <td>81.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10043</th>\n",
       "      <td>2007</td>\n",
       "      <td>29342880</td>\n",
       "      <td>43</td>\n",
       "      <td>80.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18121</th>\n",
       "      <td>2007</td>\n",
       "      <td>33152314</td>\n",
       "      <td>14</td>\n",
       "      <td>79.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16781</th>\n",
       "      <td>2007</td>\n",
       "      <td>33065250</td>\n",
       "      <td>80</td>\n",
       "      <td>79.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3026</th>\n",
       "      <td>2007</td>\n",
       "      <td>22025740</td>\n",
       "      <td>144</td>\n",
       "      <td>79.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14636</th>\n",
       "      <td>2007</td>\n",
       "      <td>31311723</td>\n",
       "      <td>222</td>\n",
       "      <td>79.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17318</th>\n",
       "      <td>2007</td>\n",
       "      <td>33087679</td>\n",
       "      <td>210</td>\n",
       "      <td>79.38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       year  school_id  number_of_students  avg_score\n",
       "16670  2007   33062633                  68      82.97\n",
       "16796  2007   33065403                 172      82.04\n",
       "16668  2005   33062633                  59      81.89\n",
       "16794  2005   33065403                 177      81.66\n",
       "10043  2007   29342880                  43      80.32\n",
       "18121  2007   33152314                  14      79.82\n",
       "16781  2007   33065250                  80      79.67\n",
       "3026   2007   22025740                 144      79.52\n",
       "14636  2007   31311723                 222      79.41\n",
       "17318  2007   33087679                 210      79.38"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import style\n",
    "style.use(\"fivethirtyeight\")\n",
    "\n",
    "df = pd.read_csv(\"./data/enem_scores.csv\")\n",
    "df.sort_values(by=\"avg_score\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at it from another angle, we can separate only the 1% top schools and study them. What are they like? Perhaps we can learn something from the best and replicate it elsewhere. And sure enough, if we look at the top 1% schools, we figure out they have, on average, a smaller number of students."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAa0AAAGECAYAAACF9X/JAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nO3de5wcVZn/8c93JgQRXCTcb3KRURAV1BWCKAlBERUkuhi8cXH56XrblYV1hSwq6wVxdb0t6q6CchPIiBIQWAwQMoSVgLeAQlwTIZBwMbgTooJcJnl+f5zToabS0zOd9Ex3Zb7v16tf03XqVPUz1dX99Kk6VUcRgZmZWRV0tTsAMzOzkXLSMjOzynDSMjOzynDSMjOzynDSMjOzynDSMjOzynDS6mCSQtK72x1HkaQJkr4j6f9yfFPbHVNNJ26vZkl6m6TfSVot6fx2x1NVks6XdMMYvdZSSWds4Dq6JP1S0jFj8fqS5kk6dz1eq1vS3ZKObHbZVnHSqiPv8CHpy3XmVf6LcQP9DfBO4ChgR+An9SpJeomkH0p6SNITkh6QdLWklxXqDEg6cUyiXk+Sdhmr5CypG/gO0As8D/jIEPUOkXSlpPtybOt8YUmaJmmRpD9Jmi3puaX5l0v62DDx1D4HjR5T1/sfHvp1uyT9k6RfS3pM0qOS7pD0mVa/Vgd5DyDgB7WCnIxq2/kJSUskfUbSxNKyrwTW+a7aUJLOlTSvWBYRq4EzgX+X1Jb84aQ1tL8AH5L0gnYH0mp1dvpm9AAPRMRPIuLhiHiqzvq3BeYCA8CbgRcCM4CfA5M24LU3djsCWwDXRsQDEbFqiHpbAHcD/ww8XJ4pScBlwHeBvwa2Af6lMP8YYDfgi8PE85EcU+2xFPj3UlndHy0b6BOkeM8GXgocDJwFbD4Kr9Up/hH4Vqx7t4fPk7bzC4DTgX8gJY21IuKRiHhsLILMrgC2Bt44hq/5jIjwo/QAzgduAG4FrizNC+DdQ03nshuA8wvTS4FPA98EVgErgA8DmwL/AawEHgA+XOe1PkL69fUY8CBwSqnOFsBX8/KPA78E3lqYv3tez7uAa/N6vjjE/y3gn4B7gKeA3wEnF+bPy+uqPZYOsZ7pef4WDbbx0tK6ap/XE4GBUt1dcp2phbJDgTuBJ/LfQ+u8N9vn9/IR4E/A/wCHFOZPzcu8Drg5b7+7gdeX3oN1/ucc0w+AP5B+4NwDfHSY/Wpyfp2/5Pf8EmC7wv9dfq2pjdZX2I5nlMq2zcs/K09/ALgmP98auB94yXp8LpYAZxamdyQlx0fz/zQP+Os62/co4Pb8Xt0FvG6Y11k41D5aqvdaYH5+31YBfcDzS5/h9wH3AX8ErgS2La3jhPyePwksBz4DTCjM34SUPB8gfSbuBt7Z6D0AjiZ9Dh/P2+Z24GUN/o/983baaQTv7Q+Anw/z+lsD3yd91n9P+u65ALih9Fk+F/g46YdPf95mm+f5Z9bZH08sLH8BcFmz+1ArHm5pNfaPwFGSDm3Buv4eWAy8AvhaflwB3Etq3p8DfE3Si0rLfZK0g72M9Kvr3yS9Fdb+ov4RsB9wLPBiUmK8TNJhpfV8nvQl+RLg60PE+EHSDn42sC/wBeBsSSfl+W8l/dJeSvrCeuUQ63ko/317g0MIrwRWAyfzzK/2EZG0E3A1qeX2cuBUUuIu1tkMuAl4DvAG0va7Frhe0j6lVX6R9Et+P+BnwKzC4bSX579/w+D/+RvAlqQvzn2Ak0hfekPFvAMwJ9c5gPRF/mKeORw0K5dD+tLbkFbMH0g/cN4oaRNSUv5lnvc14NyI+NV6rhtYu+/NBvYGjiTF/nvS9t2mVP1LwKdI78EC4CpJOzdY/UPAlEZ1JL0W+DFpHzgIOBC4kJRkal5J+jHzJuAIUnL4YmEdbyIdjr2I9Lk4FfgQ6TNXcxbwXtJ++mLgYuDiOp+v2jp3ICWMS0mfoYOAr5COOgxlCunoxYMN6pAPrb+alDwb+S5pXz4SmEb6gTW9Tr1jSEc+ppIO+U8ntd4hbadLSD/ca5/PWYVlbyNt27HXjkzZ6Q/yr7T8/FLSB74rT69vS2t2YbqL9MvvR6WylRRaW3ndF5XWfQlwS34+lfTrdctSne/UXo9nWlofH8H/vQz4t1LZl4F7CtNnAktGsK5PkT5cfyQljzOBvUt1Bij8estlJzJMS4v0a/g+Bv8iPrL4XuT1LC/WyeVzga8Utl8wuGW6Qy57fb3XLtS7g0KrYwTb49M5nomFsv3yug8pvVevbmK9Syn9Gs/lryIliPtIv4q3yNtoIemL6nxS6/BKYPsRvtbalhZwWI71RYX5m5ISzidK2/ekQp0JOabPNHidvYFfA2uA/83xv6v0fs8Hrh7mM/wIsGmh7DTgodI6ekvLfYTUapwIPJvUAvtgqc4VwNx67wEpMQewexPv4VeA24Z4b58E/pz/BukzM32ofYB0+D6AwwrzNyF9tsstrTtL6/lP4NbC9LnAvCFifnN+nc1H+n+26uGW1vBOI32ITtzA9dxRexIRa0gfqDtLZSuA7UrL3Vqa/h+g1hp7JenD9YCkP9cewLtJO2/R7Y2Ck/RXpC/om0uz+oDdJT270fJlEfEJ0uG5E0lfnn8D3Cnpnc2sZwgvAm6PiOKv11tKdV5JSkCPlrbNa1h32ywsxP0wqQW4/TAxfAWYKek2SZ+XdMgw9fcFFkThHGBE3EE6rLXvMMs2LdI5x8kRsVtEnAB0k1rz7yHt05uQzpP8L6n11ax9gf+LiLsLr/kk6Rd4+f+5tVBngLQvlo8oFGP/Danl84oc80TSF+iC3IImz5szTIyLckw1DzD4fd2X+vv7s4DnA3vl165XZ6j37E5SC/DXkq6Q9BFJuw4T52akH5/1fJ3UQnw1cBVwTkTMbrCu2nZdUCuIiKdJRxDKFpamy9unkVq8mzWsNQqctIYREfeRWhufkbRFvSqkc0FFm9Sp93Sd5eqVDfeeFF+ri/Slt3/p8SLSIbGikZ6ojQav15SIWBkRP4yI00kn1OcBnx1msTV1ysrbU6wbZ3m6C1jEuttmH9LhnqJ6h1savg8R8V1SZ4b/JB06+W9JFzdapk6Mw5W30peA70XEL0mHNC/JCeTCPL0+6sVd772pV6fxipNfRsR/RMQ7SIc4X0Hq0NPo9YvK72u9z+pQ+3sMU6fua0fqXfcG0mG5n5J+rP12mC7ijzB0B6X+iFgSET8l/e/TJR3fYF1DxVxPve0z0pwwifTjrn+E9VvGSWtkPkfaVvW6CK8AdqpNSNqUBr8i18Pk0vRBpC9jSL+enks64b6k9Li/mReJiD+SDl9NKc06BLg3Ih5fj9iL6w/Sr/piS/IpUgugaAXQLan4i+/lpTp3AQfmLuI1ry7V+RmwJ/DHOtum4bmDktoHuxwnEfFQRHw3Io4nndN6V26x1nMXcFCx56ak/Ujnxe5qIp6mSXod6ZzPp3JRF8/8EJjI+n0P3AVsUzwHm/f9A1j3/5lcqDOB1ApeRHNq9Wv7z8+B1ze5jrK7qL+/1zrWLCEdlqtXZ8j3LCfc2yPirIg4hNQye0+DOH4B9AzXqze3Gs8indceqidlreV7UK0gb/NXNFr3EOp9PmteAvwyHyEaU05aIxARfyL1sjm1zuwbgPdLOkjSi0nH0jekS3nZkZI+LKlH0t+TOlzUrsmYm1//h5LeImlPSa+Q9PeSyq2Jkfgc8PeS3ptf7+9IPc/OamYlko6SdImkN0t6YV7Xe4G/JZ0PqLkXOFTSToWT97eTevqdnZc7gtQFuuibpB5y35K0Tz4pXm7BfS+v/xpJh0vaXdKBkk6XVO+k9FD+QDqncLikHSRtlf/HcyS9UdLzJe1L6qSyLMdezznAXwHnS3qxpFeTOgDcEhHzm4gHSVtI2l/S/qR9bYc8vVe9uqTW4EmFQ2U3Ax+W9ELgFNKXarPmkt6rSyQdnPf9C0mH1r5Zqnta3lb75Hnb16lTjPkHkk7Nn6ndJL2KtK2eBq7J1T4NvEHSVyS9NO9nJ+b/aaQ+B/yNpNMkvUDSDPI1SBHxVP6h9jXg00oXffdImknqKFP3MyHpVZI+nve15+V986U8k0zquYnUyjlwBDFfmP+eXG9mRCwmdc76uqQp+UfFf5H2vWZb9PcCe0vaV9I2+UdJzVSeeS/G1lifRKvCg0JHjEJZF+m8VLkjxg6kneSPpC+tD1C/I0a56+qg7sO57DcUTlDn1zqZ1EvrcdJJ7o+WltmM1NvvXtIvo4eB64Bpef7ujPDkPumwx0fzup4m/do8uVTnTIbpiEFq4XyT9EH9M+mL/Neka282K9Q7gvQL+klyYyyXvymX/4V0Du/1rNvl/TDgV3nZX5MOx5Tfm61zHLXuyg+QkubL8vypeZldSvEP6iACHF/YJktz2deB3+YY/4/0Ad53mO1S7PL+KIUu7828V4W4y495deqeQ6n7eN4uP8rvy83A80b4uRiuy3sf9bu8v5nUMnqS0iUFQ7zOe4HrSfv7k/l9mw0cVKr3etL5sr+QDpPfBOzZ4DP87uJ+lstOyPtabf/4LBvQ5Z10ruta0ufwSVKnky9Q6IAzxP/8XdJ1WnXXWyr/l7zNJ9Wrl9/fy0nfGStILezvM7jj1zxSL9Lies+gcBkL6RDgtXnbBvkzQfp8Pw3sOpL9ptUP5SDMzFpK6W4ZN5G+3Ia8HMBA0vNJh7T3jeYOX49k3d2kH8RXRUS9o0XNru8bgCLiAxsc3HqY0I4XNTOzZ0TE7/Lh+D1I19itt9yTdTvSpTrPIV1vujup9blBlK67XA58a0PXtb6ctMzMOkBE9LZoVd2kQ317kQ7j/Ro4NDbwgnJYe2lOU+e4W82HB83MrDLce9DMzCqjsocHV61a5SaimdlGbMstt1znQnS3tMzMrDKctMzMrDKctMzMrDKctMzMrDKctMzMrDKctMzMrDLGLGlJWirpV5IWSvpZLpsk6XpJi/Pf2h20JelrkpZIulNSeWgKMzMbh8a6pXVoROwfEX+dp08DboyIHuDGPA1pELWe/HgfDYYxMDOz8aPdhwePBi7Izy8AphfKL4xkAfBcSTu2I0AzM+scY5m0Apgj6eeS3pfLto+IhyCNAsszo5LuTBqbqmZ5LjMzs3FsLG/jdHBEPChpO+B6Sb9pUHedW3fQYNTNxYsXb3BwZmbWfj09PQ3nj1nSqg1sFhErJF0BHAD8XtKOEfFQPvy3IldfDuxaWHwXGowxM9w/aa1z+eWXc/HFF3PCCSfwlre8pd3hmNk4MyaHByVtLuk5tefA4aQxXq4iDXdN/ntlfn4VcHzuRTgZWFU7jGjtdfHFFwNwwQUXDFPTzKz1xuqc1vbALZLuAG4HromI64CzgddJWgy8Lk8DXAvcAywBvg18cIzitAYuv/zyQdNXXHFFmyIxs/GqsoNAemiSsTd9+vR1ymbPnt2GSMxsPPDQJGZmVmlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmdfT39zNz5kxWrlzZ7lCswEnLzKyO3t5eFi1axKxZs9odihU4aZmZlfT393PjjTcSEdx4441ubXUQJy0zs5Le3l4GBgYAGBgYcGurgzhpmZmVzJs3j4gAICKYN29eewOytZy0zMxKtt1224bT1j5OWmZmJY888kjDaWsfJy0zs5KpU6c2nLb2cdIyMys5/PDDB00fccQRbYrEypy0zMxK5syZM2j6uuuua1MkVuakZWZW0tfX13Da2sdJy8ys5MADDxw0PXny5DZFYmVOWmZmJZIaTlv7OGmZmZUsWLBg0PStt97apkiszEnLzKxkypQpdHd3A9Dd3c2UKVPaHJHVOGmZmZXMmDFjUNI69thj2xyR1ThpmZmVTJo0iWnTpiGJadOmsdVWW7U7JMsmtDsAM7NONGPGDO6//363sjqMW1pmZlYZTlpmZnV45OLO5KRlZlbS39/P3LlziQjmzp3rkYs7iJOWmVlJb28va9asAWDNmjVubXUQJy0zs5K+vj4GBgYAGBgY8L0HO4iTlplZyZQpU5gwIXWunjBhgi8u7iBOWmZmJTNmzKCrK309dnV1udt7B3HSMjMr8cXFncsXF5uZ1eGLizuTk5aZWR2TJk3irLPOancYVuLDg2ZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhlOWmZmVhljmrQkdUv6paSr8/Qekm6TtFjSLEkTc/mmeXpJnr/7WMZpZmadaaxbWh8BFhWmPw98OSJ6gJXASbn8JGBlROwFfDnXMzOzcW7MkpakXYA3AefmaQHTgMtzlQuA6fn50XmaPP+wXN/MzMaxsWxpfQX4Z2BNnt4aeDQiBvL0cmDn/HxnYBlAnr8q1zczs3FsTO7yLulIYEVE/FzS1FpxnaoxgnnrWLx48YYFaOvN297MWqmnp6fh/LEamuRg4M2S3gg8C/grUsvruZIm5NbULsCDuf5yYFdguaQJwJZA/1ArH+6ftNHjbW9mY2lMDg9GxOkRsUtE7A68HZgbEe8CbgKOydVOAK7Mz6/K0+T5cyNiyJaWmZmND+2+TutjwCmSlpDOWZ2Xy88Dts7lpwCntSk+Mxun+vv7mTlzJitXrmx3KFYw5kkrIuZFxJH5+T0RcUBE7BURb4uIJ3P5E3l6rzz/nrGO08zGt97eXhYtWsSsWbPaHYoVtLulZWbWcfr7+5k7dy4Rwdy5c93a6iBOWmZmJb29vaxevRqA1atXu7XVQZy0zMxK+vr6BiWtvr6+NkdkNU5aZmYlBx544KDpyZMntykSK3PSMjMreeqppxpOW/s4aZmZldx2222DphcsWNCmSKzMScvMzCrDScvMrOSQQw4ZND1lypQ2RWJlTlpmZiXHHXfc2ueSBk1bezlpmZnV4SH8OpOTlplZSW9vL11d6euxq6vLFxd3ECctM7MSX1zcuZy0zMxKpkyZsvbwoCR3xOggTlpmZiWHH344tSH8IoIjjjiizRFZjZOWmVnJnDlzBrW0rrvuujZHZDVOWmZmJX19fYNaWj6n1TmctMzMSqZMmcKECRMAmDBhgs9pdRAnLTOzkhkzZgzq8n7ssce2OSKrcdIyMyuZNGkS06ZNQxLTpk1jq622andIlk1odwBmZp1oxowZ3H///W5ldRgnLTOzOiZNmsRZZ53V7jCsxIcHzcysMpy0zMysMpy0zMysMpy0zMysMlS76rtqVq1aVc3AmzB9+vR2h1AZs2fPbncIZtZiW2655TqDmrmlZWZWR39/PzNnzmTlypXtDsUKnLTMzOro7e1l0aJFHgCywzhpmZmV9Pf3M3fuXCKCuXPnurXVQTbo4mJJhwKrI+LmFsVjBZ12nqZ8jm277bbjW9/6VpuiMRs9vb29rFmzBoA1a9Ywa9Ys3v/+97c5KoMmW1qS+iQdnJ9/DLgMuFTSzNEIzjqbE5ZtrPr6+hgYGABgYGDAQ5N0kGYPD74YWJCfvxeYCkwG/BPEzDYaU6ZMobu7G4Du7m4PTdJBmk1aXUBIej6pu/yiiFgG+BbIZrbRmDFjxqBBIH3T3M7R7DmtW4BzgB2BKwByAvtDi+MyM2urYtKyztFsS+tE4FHgTuCTuWxv4KstjMnMrK16e3sHJS13e+8czSataRExMyI+GRGPAUTENcDy1odmZtYe8+bNazht7dNs0jpviHJ3IzOzjca2227bcNraZ0TntCTtmZ92SdoDKN4Pak/giVYHZmbWLo888kjDaWufkXbEWAIEKVn9rjTvYeDMFsZkZtZWkydPHnRI8KCDDmpfMDbIiJJWRHRBurg4InzBgplt1J566qmG09Y+TZ3TcsIys/HgtttuGzS9YMGCIWraWGvqOq18PuuzwP7AFsV5EfG8FsZlZma2jmYvLr6EdE7rVODx1odjZtZ+r3nNawad0zrkkEPaF4wN0mzS2hc4OCLWjEYwZmad4Pjjjx+UtI4//vj2BWODNHud1s3Ay0YjEDOzTiJp0F/rDM22tJYCP5b0Q1JX97Ui4hOtCsrMrJ16e3vp6upi9erVdHV1eTytDtJsS2tz4EfAJsCupYeZ2Uahr6+P1atXA7B69WqPp9VBmmppRcR7RisQM7NOMWXKFG644QYGBgaYMGGCx9PqIM22tJC0j6SPSzonT79Q0ktbH5qZWXvMmDGDrq709djV1eXxtDpIU0lL0ttInTF2BmrdaZ4DfKnFcZmZtc2kSZN41ateBcDBBx/MVlt5nNtO0WxL61PA6yLi/cDqXHYHsF9LozIzazP3HuxMzSat7UhJCtINdGt/PbSnmW00+vv7ueWWWwCYP38+K1eubHNEVtNs0vo5cFyp7O3A7a0Jx8ys/Xp7exkYGABgYGDAIxd3kGaT1j8An5HUB2wu6cfAp4F/bLSQpGdJul3SHZLukvSvuXwPSbdJWixplqSJuXzTPL0kz9+96f/MzGw9zZs3j4h0ACkiPHJxB2n2Lu+/AfYGvg6cAXwXeElELB5m0SeBaRGxH+lmu0dImgx8HvhyRPQAK4GTcv2TgJURsRfw5VzPzGxMeOTiztV0l/eIeDwieiPiCxFxWUT8eQTLRKHeJvkRwDTg8lx+ATA9Pz86T5PnHyafDTWzMeKRizvXsBcXS5rPCDpaRETD2yBL6iadE9uL1FL7HfBoRAzkKstJXenJf5fl9Q5IWgVsDfxhuDjMzDbU1KlTue666wZNW2cYyR0xzi08fz7wt6RW0H3A84ATgO8Mt5KIWA3sL+m5wBXAPvWq5b/1WlVDJs7Fi4c7OmmjwdvdNlZ77733oKS1zz77eH8fIz09PQ3nD5u0IqJ2mA5JC4DXR8RdhbJLSEnrkyMJKCIelTQPmAw8V9KE3NraBXgwV1tOup/hckkTgC2B/qHWOdw/aaPD2902Vtdcc82g6YULF/pWTh2i2XNa+5AO6xXdS+qcMSRJ2+YWFpI2A14LLAJuAo7J1U4ArszPr8rT5Plzo9aVx8xslM2fP3/Q9M0339ymSKys2aTVB5wvqUfSZpJeAJwHzB9muR2BmyTdCfwUuD4irgY+BpwiaQnpnNV5uf55wNa5/BTgtCbjNDOzjVCz42mdCHwDuAvoBgaAHwIN7/4eEXdSZ/DIiLgHOKBO+RPA25qMzcysJQ488EB+8pOfrJ2ePHlyG6OxomaHJukH3i6pC9gWeCQi1oxKZGZmbTJx4sSG09Y+zd7lfU9JewK7kwaE3L1QZma2UbjtttsGTS9YsKBNkVhZs4cHl5C6nhe7pNc6SHS3JCIzszabPHkyN91009rpgw46qI3RWFGzhwcHtcwk7UDq6j5cRwwzs8ood1Z25+XO0fRtnIoi4mHgZOBzrQnHzKz9yocDb7311jZFYmUblLSyFwLPbsF6zMw6gm+Y27maOjxY5z6Ezwb2JY1obGa2UVixYkXDaWufZjtinFuafgy4YwRDk5iZVcZ2223HsmXLBk1bZ2g2aT0eEd8vF0o6JiIur7eAmVnVeGiSztXsOa3zhij/1oYGYmbWKcpDkXhoks4xoqRVuIC4S9Ieten8eC3wxOiGaWY2dg4//PBB00cccUSbIrGykba0lgCLSR0vfpena48LgTNHIzgzs3aYM2cOtcHSJQ0aW8vaa0RJKyK6IqIbmJ+fFx87RYQPD5rZRqOvr2/tBcURQV9fX5sjspqmzmlFxKBR0PLhwd1aG5KZWXtNmTKF7u50Z7ru7m4PANlBmr1h7qWSXpWfv4c0RMndkk4ajeDMzNphxowZrFmTBrBYs2YNxx57bJsjsppmew8eBvwsPz+FNALxAXiQRjPbyPh+g52p2aQ1MSKekrQzMCki/ici7gK2H4XYzMza4qKLLlr7PCIGTVt7NZu0Fko6Hfg4cA1ATmB/bHVgZmbtcvPNNw+adkeMztFs0joJeAmwGXBGLjsI+F4rgzIzM6un2fG0fge8s1R2ObD2Fk6SvhERH2xNeGY2XkyfPr3dIQxp9erVHRXf7Nmz2x1C27RiaJKyd4/COs3MzEYlaWkU1mlmZjYqScv9RM3MbFQ0OzSJmdmo6KTzNOXzV50U23jnw4NmZlYZwyYtSbMKz98zgnVevEERmZmZDWEkLa3Xq3aPfvjqcJUj4gMbFpKZmVl9IzmnNR+4VdJvgWdJurBepYg4vqWRmZmZlYwkab0NOAbYjdQz8HejGpGZmdkQhk1aEfEE+TyVpE0i4l9HPSozM7M6mr2N05mSeoB3ADsDDwCXRsTi0QjOzMysqNlBII8Cfg7sDfQDLwR+JunNoxCbmZnZIM1eXHwWcHRE3FQrkDQVOAe4qoVxmZmZraPZi4t3IfUmLLoll5uZmY2qpgeBBE4tlZ2Sy83MzEZVs4cHPwD8SNJHgGXArsBjgM9pmZnZqGu29+BvJO0DTAZ2Ah4EbouIp2t1JO0SEctbG6aZmdl63OU9IgZI57GGcjfwV+sdkZmZ2RB8l3czM6sMDwJpZmaVMRpJy8zMbFQ4aZmZWWU0exunkdT3OS0zMxsVI05akrqBxyRtOkzVF21YSGZmZvWNOGlFxGrgt8DWw9RbtqFBmZmZ1dPsdVrfA66W9FVgOYWeghExt5WBmZmZla3PbZwAziyVB7DnBkdjZmbWQLO3cdpjtAIxMzMbTtNd3iVtIuk1ko7N05tL2rz1oZmZmQ3WbJf3l5A6Y3wbOC8XTwG+0+K4zMzM1tFsS+ubwCciYm+gdmf3PuDVLY3KzMysjmaT1r7Axfl5AETEY8BmrQzKzMysnmaT1lLgFcUCSQcASxotJGlXSTdJWiTprjyIJJImSbpe0uL8d6tcLklfk7RE0p2SXt5knGZmthFqNml9HLhG0r8CEyWdDnwfOGOY5QaAUyOiNoDkhyS9CDgNuDEieoAb8zTAG4Ce/Hgf6bCkmZmNc00lrYi4mpRQtiWdy9oNeGtEzBlmuYci4hf5+Z+ARcDOwNHABbnaBcD0/Pxo4MJIFgDPlbRjM7GamdnGZ31GLv4F8MH1fUFJuwMvA24Dto+Ih/J6H5K0Xa62M1C8HdTyXPbQ+r6umabVHnUAAAzNSURBVJlVX1NJS9JE0qHAdwA7AQ8ClwGfjYgnRrD8FsAPgJMj4o/SkDeErzdjyMElFy9ePNxL2yjwdrfxwvv62Onp6Wk4v9mW1jeBFwL/ANxHOjx4OqkV9LeNFpS0CSlhfS8ifpiLfy9px9zK2hFYkcuXA7sWFt+FlCDrGu6ftNHh7W7jhff1ztFsR4zpwJER8d8RcXdE/Hcum95oIaUm1XnAooj4UmHWVcAJ+fkJwJWF8uNzL8LJwKraYUQzMxu/mm1pPQw8G3i0ULYZw59rOhg4DviVpIW5bCZwNtAr6STgfuBted61wBtJXekfB97TZJxmZrYRGjZpSZpWmLwIuE7Sf/DMIbwPARc2WkdE3MLQIxofVqd+5PWamZmtNZKW1nl1ymaWpv8O+PyGh2NmZja0YZOWhyMxM7NO0fTQJGZmZu3S7NAk+0maK6lf0lP58bSkp0YrQDMzs5pmew9eSrrW6h+Av7Q+HDMzs6E1m7R2II2nNeTdKczMzEZLs+e0LgDeORqBmJmZDafZltbZwK2SZgK/L86IiGn1FzEzM2uNZpPW5cC9wBX4nJaZmY2xZpPW/sDWEbFR9BacPr3hLRNtGN5+Izd79ux2h2C2UWj2nNZ84EWjEYiZmdlwmm1p3QvMkXQF657T+kTLojIzM6uj2aT1bOAaYCKDx7syMzMbdU0lrYjYqIcIWXx4+T7AZuunZ85Z7Q7BbKPUVNKStOdQ8yLing0Px8zMbGjNHh5cAgSDx8aq3R2juyURmZmZDaHZw4ODehtK2gH4JKlXoZmZ2ajaoKFJIuJh4GTgc60Jx8zMbGitGE/rhaRehWZmZqOq2Y4Y83nmHBbA5qSLjT/dyqDMzMzqabYjxrml6ceAOyJicYviMTMzG1KzSesy4ATSPQi3yGVvlkREHN/SyMzMzEqaTVrnA/sBP6J0GyczM7PR1mzSOgLYIyIeHY1gzMzMGmm29+D9wKajEYiZmdlwmm1pXQhcKemrrHuX97kti8rMzKyOZpPWh/Pf8t1AAxjyvoRmZmat0OxtnPYYrUDMzMyG04o7YpiZmY0JJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6uMZi8uNrOKmj59ertDqCxvu+bMnj171NbtlpaZmVWGk5aZmVWGk5aZmVWGz2mZjVMX7bFZu0OwjcRx9/5lzF7LLS0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6uMMblhrqTvAEcCKyLixblsEjAL2B1YCsyIiJWSBHwVeCPwOHBiRPxiLOLsmXPWWLyMmZmtp7FqaZ0PHFEqOw24MSJ6gBvzNMAbgJ78eB/wzTGK0czMOtyYJK2IuBnoLxUfDVyQn18ATC+UXxjJAuC5knYcizjNzKyztfOc1vYR8RBA/rtdLt8ZWFaotzyXmZnZONeJg0CqTlk0WmDx4sUteeHFh89syXrMyudHW7WPmlXBhuzvPT09Dee3M2n9XtKOEfFQPvy3IpcvB3Yt1NsFeLDRiob7J83azfuojSejub+38/DgVcAJ+fkJwJWF8uOVTAZW1Q4jmpnZ+DZWXd4vBaYC20haDnwSOBvolXQScD/wtlz9WlJ39yWkLu/vGYsYzcys841J0oqIdwwx67A6dQP40OhGZGZmVeQ7YpiZWWU4aZmZWWU4aZmZWWU4aZmZWWU4aZmZWWU4aZmZWWU4aZmZWWV04r0HzWwMHHfvX9odglnT3NIyM7PKcNIyM7PKcNIyM7PK8Dkts3Hqoj02a3cItpEYy/OjbmmZmVllOGmZmVllOGmZmVllOGmZmVllOGmZmVllOGmZmVllOGmZmVll+Dqtgp45Z7U7BDMza8AtLTMzqwwnLTMzqwwnLTMzq4xxfU5r9uzZ7Q6hUqZPnz5o2tvPzMaaW1pmZlYZTlpmZlYZ4/rwoNl4NpbDSZi1iltaZmZWGU5aZmZWGU5aZmZWGT6nZTZO+BKFkfPlHZ3LLS0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMJy0zM6sMj1xsZh2hPFpwJ+m02MbzSMpOWh2s0z4oZZ0U33j+EJuNJz48aGZmleGkZWZmldGxhwclHQF8FegGzo2Is9sckpmNIh/itZFQRLQ7hnVI6gZ+C7wOWA78FHhHRNxdq7Nq1arOC9zMzFpmyy23VLmsUw8PHgAsiYh7IuIp4DLg6DbHZGZmbdapSWtnYFlhenkuMzOzcaxTz2mt0yQEhjwcuHjx4lEMxczMxkpPT0/D+Z2atJYDuxamdwEeHKrycP+kmZltHDr18OBPgR5Je0iaCLwduKrNMZmZWZt1ZEsrIgYkfRj4ManL+3ci4q42h2VmZm3WkV3eR8Jd3s3MNm5V6vJuZma2DictMzOrDCctMzOrDCctMzOrDCctMzOrDCctMzOrDCctMzOrjMpep2VmZuOPW1pmZlYZHXkbJxtbklYDvyoUTY+IpUPU/XNEbDEmgZmNEklbAzfmyR2A1cAjefqAPI6fdSAfHrSmEpGTlm1sJJ0J/DkivlgomxARA+2Lyobiw4O2DklbSLpR0i8k/UrSOqNGS9pR0s2SFkr6taTX5PLDJd2al/2+JCc4qwRJ50v6kqSbgM9LOlPSPxXm/1rS7vn5uyXdnvf//5LU3aawxx0nLQPYLH/4Fkq6AngCeEtEvBw4FPh3SeUbV74T+HFE7A/sByyUtA1wBvDavOzPgFPG7t8w22AvIO2/pw5VQdI+wLHAwXn/Xw28a4ziG/d8TssA/pI/fABI2gQ4S9IhwBpgZ2B74OHCMj8FvpPrzo6IhZKmAC8C/ifnuInArWP0P5i1wvcjYvUwdQ4DXgH8NO/nmwErRjswS5y0rJ53AdsCr4iIpyUtBZ5VrBARN+ek9ibgIklfAFYC10fEO8Y6YLMWeazwfIDBR6NqnwEBF0TE6WMWla3lw4NWz5bAipywDgV2K1eQtFuu823gPODlwALgYEl75TrPlvSCMYzbrJWWkvZrJL0c2COX3wgcI2m7PG9S/jzYGHBLy+r5HvAjST8DFgK/qVNnKvBRSU8DfwaOj4hHJJ0IXCpp01zvDOC3ox+yWcv9ADhe0kLS4fDfAkTE3ZLOAOZI6gKeBj4E3Ne2SMcRd3k3M7PK8OFBMzOrDCctMzOrDCctMzOrDCctMzOrDCctMzOrDCcts4qTdKKkW0ZhvVMlLW/1es02hJOWWRMkLZX02nbHYTZeOWmZmVllOGmZjZCki4Dnke4W8mdJ/yzpzZLukvSopHn5DuC1+kslnS7pbkkrJX1X0rOGfgWQtI2kq/P6+iXNz3ddQNKukn4o6RFJ/yfpnNKyX8yvc6+kNxTKd5J0VV7fEknvLczbVNJXJD2YH18p3M3ErOM4aZmNUEQcB9wPHJUHwpwNXAqcTLrB8LWkhDaxsNi7gNcDzycNe3HGMC9zKrA8r297YCYQebymq0m3CtqddOf9ywrLHQj8L7AN8G/AeYXhZC7N69wJOIZ0B//D8rx/ASYDtSFmDhhBjGZt46Rltv6OBa6JiOsj4mngi6RhKl5VqHNORCyLiH7gs8Bwd8B/GtgR2C0ino6I+ZHutXYAKel8NCIei4gnIqLY+eK+iPh2HlbjgryO7SXtCrwa+FheZiFwLnBcXu5dwKciYkVEPAL8a2GeWcdx0jJbfztRuElqRKwBlpFaQTXLCs/vy8s08gVgCelmrPdIOi2X70pKTEMNAb92rLOIeDw/3SK/Xn9E/KkURy3GQf/DCGM0axsnLbPmFO8w/SCFYVvy4bhdgQcKdXYtPH9eXmbolUf8KSJOjYg9gaOAU/KhvGXA8yQ1OzLDg8AkSc8pxfFAYf5upXkNYzRrJycts+b8HtgzP+8F3iTpsDyC86nAk8BPCvU/JGkXSZNI56dmNVq5pCMl7ZUT4B9JQ7mvBm4HHgLOlrS5pGdJOni4YCNiWY7nc3mZlwInkYafgXS+6wxJ20raBvgEcPEItoNZWzhpmTXnc6Qv+UdJLaF3A/8B/CFPHxURTxXqXwLMAe7Jj88Ms/4e4AbSGGW3At+IiHn5XNVRwF6kziDLSefURuIdpM4bDwJXAJ+MiOvzvM8APwPuBH4F/GIEMZq1jcfTMhslkpYC/y8ibmh3LGYbC7e0zMysMpy0zMaYpJn54uTy47/bHZtZp/PhQTMzqwy3tMzMrDKctMzMrDKctMzMrDKctMzMrDKctMzMrDKctMzMrDL+P77HDexC89YRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = (df\n",
    "             .assign(top_school = df[\"avg_score\"] >= np.quantile(df[\"avg_score\"], .99))\n",
    "             [[\"top_school\", \"number_of_students\"]]\n",
    "             .query(f\"number_of_students<{np.quantile(df['number_of_students'], .98)}\")) # remove outliers\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "sns.boxplot(x=\"top_school\", y=\"number_of_students\", data=plot_data)\n",
    "plt.title(\"Number of Students of 1% Top Schools (Right)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One natural conclusion that follows is that small schools lead to higher academic performance. This makes intuitive sense, since we believe that less students per teacher allows the teacher to give focused attention to each student. But what does this have to do with Moivre’s equation? And why is it dangerous? \n",
    "\n",
    "Well, it becomes dangerous once people start to make important and expensive decisions based on this information. In his article, Howard continues:\n",
    "\n",
    "\"In the 1990s, it became popular to champion reductions in the size of schools. Numerous philanthropic organisations and government agencies funded the division of larger schools based on the fact that students at small schools are over represented in groups with high test scores.\"\n",
    "\n",
    "What people forgot to do was to look also at the bottom 1% of schools. If we do that, lo and behold! They also have very few students!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_99 = np.quantile(df[\"avg_score\"], .99)\n",
    "q_01 = np.quantile(df[\"avg_score\"], .01)\n",
    "\n",
    "plot_data = (df\n",
    "             .sample(10000)\n",
    "             .assign(Group = lambda d: np.select([d[\"avg_score\"] > q_99, d[\"avg_score\"] < q_01],\n",
    "                                                 [\"Top\", \"Bottom\"], \"Middle\")))\n",
    "plt.figure(figsize=(10,5))\n",
    "sns.scatterplot(y=\"avg_score\", x=\"number_of_students\", hue=\"Group\", data=plot_data)\n",
    "plt.title(\"ENEM Score by Number of Students in the School\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we are seeing above is exactly what is expected according to the Moivre’s equation. As the number of students grow, the average score becomes more and more precise. Schools with very few samples can have very high and very low scores simply due to chance. This is harder to occur with large schools. Moivre’s equation talks about a fundamental fact about the reality of information and records in the form of data: it is always imprecise. The question then becomes how much imprecise.\n",
    "\n",
    "Statistics is the science that deals with these imprecisions so they don't catch us off-guard. As Taleb puts it in his book, Fooled by Randomness:\n",
    "\n",
    "> Probability is not a mere computation of odds on the dice or more complicated variants; it is the acceptance of the lack of certainty in our knowledge and the development of methods for dealing with our ignorance.\n",
    "\n",
    "One way to quantify our uncertainty is the **variance of our estimates**. Variance tells us how much observation deviates from their central and most probably value. As pointed by the Moivre’s equation, this uncertainty shrinks as the amount of data that we observe increases. This makes sense right? If we see lots and lots of students performing excellent at a school, we can be more confident that this is indeed a good school. However, if we see a school with only 10 students and 8 of them perform well, we need to be more suspicious. It could be that, by chance, that school got some above average students.\n",
    "\n",
    "The  beautiful triangular plot we see above tells exactly this story. It shows us how our estimates of the school performance has a huge variance when the sample sizes are small. It also shows that variance shrinks as the sample size increases. This is true for the average score in a school, but it is also true about any summary statistics that we have, including the ATE we so often want to estimate.\n",
    "\n",
    "##  The Standard Error of Our Estimates\n",
    "\n",
    "Since this is just a review on statistics, I'll take the liberty to go a bit faster now. If you are not familiar with distributions, variance and standard errors, please, do read on, but keep in mind that you might need some additional resources. I suggest you google any MIT course on introduction to statistics. They are usually quite good.\n",
    "\n",
    "In the previous section, we estimated the average treatment effect \\\\(E[Y_1-Y_0]\\\\) as the difference in the means between the treated and the untreated \\\\(E[Y|T=1]-E[Y|T=0]\\\\). As our motivating example, we figured out the \\\\(ATE\\\\) for online classes. We also saw that it was a negative impact, that is, online classes made students perform about 5 points worse than the students with face to face classes. Now, we get to see if this impact is statistically significant.\n",
    "\n",
    "To do so, we need to estimate the \\\\(SE\\\\). We already have \\\\(n\\\\), our sample size. To get the estimate for the standard deviation we can do the following\n",
    "\n",
    "$\n",
    "\\hat{\\sigma}=\\frac{1}{N-1}\\sum_{i=0}^N (x-\\bar{x})^2\n",
    "$\n",
    "\n",
    "where \\\\(\\bar{x}\\\\) is the mean of \\\\(x\\\\). Fortunately for us, most programming software already implements this. In Pandas, we can use the method [std](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.std.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SE for Online: 1.5371593973041635\n",
      "SE for Face to Face: 0.8723511456319106\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/online_classroom.csv\")\n",
    "online = data.query(\"format_ol==1\")[\"falsexam\"]\n",
    "face_to_face = data.query(\"format_ol==0 & format_blended==0\")[\"falsexam\"]\n",
    "\n",
    "def se(y: pd.Series):\n",
    "    return y.std() / np.sqrt(len(y))\n",
    "\n",
    "print(\"SE for Online:\", se(online))\n",
    "print(\"SE for Face to Face:\", se(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence Intervals\n",
    "\n",
    "The standard error of our estimate is a measure of confidence. To understand exactly what it means, we need to go into turbulent and polemic statistical waters. For one view of statistics, the frequentist view, we would say that the data we have is nothing more than a manifestation of a true data generating process. This process is abstract and ideal. It is governed by true parameters that are unchanging but also unknown to us. In the context of the students test, if we could run multiple experiments and collect multiple datasets, all would resemble the true underlying data generating process, but wouldn't be exactly like it. This is very much alike Plato's writing on the Forms:\n",
    "\n",
    "```\n",
    "Each [of the essential forms] manifests itself in a great variety of combinations, with actions, with material things, and with one another, and each seems to be many\n",
    "```\n",
    "\n",
    "To better grasp this, let's suppose we have a true abstract distribution of students' test score. This is a normal distribution with true mean of 74 and true standard deviation of 2. From this distribution, we can run 10000 experiments. On each one, we collect 500 samples. Some experiment data will have a mean lower than the true one, some will be higher. If we plot them in a histogram, we can see that the true mean is where most of the experiments' mean fall in. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_std = 2\n",
    "true_mean = 74\n",
    "\n",
    "n = 500\n",
    "def run_experiment(): \n",
    "    return np.random.normal(true_mean,true_std, 500)\n",
    "\n",
    "np.random.seed(42)\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "freq, bins, img = plt.hist([run_experiment().mean() for _ in range(10000)], bins=40, label=\"Experiment's Mean\")\n",
    "plt.vlines(true_mean, ymin=0, ymax=freq.max(), linestyles=\"dashed\", label=\"True Mean\")\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we are talking about the mean of means here. So, by chance, we could have an experiment where the mean is somewhat below or above the true mean. This is to say that we can never be sure that the mean of our experiment matches the true platonic and ideal mean. However, **with the standard error, we can create an interval that will contain the true mean 95% of the time**.\n",
    "\n",
    "In real life, we don't have the luxury of simulating the same experiment with multiple datasets. We often only have one. But we can drawn on the intuition above to construct what we call **confidence intervals**. Confidence intervals come with a probability attached to them. The most common one is 95%. This probability tells us how many of the hypothetical confidence intervals we would build from different studies contains the true mean. For example, the 95% confidence intervals computed from many similar studies would contain the true mean 95% of the time. \n",
    "\n",
    "To calculate the confidence interval, we use what is called the **central limit theorem**. This theorem states that **means of experiments are normally distributed**. From statistical theory, we know that 95% of the mass of a normal distribution is between 2 standard deviations above and below the mean. Technically, 1.96, but 2 is close enough. \n",
    "\n",
    "![normal_density](./data/img/stats-review/normal_dist.jpeg)\n",
    "\n",
    "The Standard Error of the mean serves as our estimate for the means' distribution of our experiments. So, if we multiply it by 2 and add and subtract it from one of our experiment's mean, we will construct a 95% confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(73.82718114045632, 74.17341543460314)\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(321)\n",
    "exp_data = run_experiment()\n",
    "exp_se = exp_data.std() / np.sqrt(len(exp_data))\n",
    "exp_mu = exp_data.mean()\n",
    "ci = (exp_mu - 2 * exp_se, exp_mu + 2 * exp_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we don't need to restrict ourselves to the 95% confidence interval. We could generate the 99% interval by finding how many times do we need to multiply the standard deviation so the interval contains 99% of the mass of a normal distribution. \n",
    "\n",
    "The function `ppf` in python gives us the inverse of the CDF. So, `ppf(0.5)` will return 0.0, saying that 50% of the mass of the standard normal distribution is below 0.0. By the same token, if we plug 99.5%, we will have the value `z`, such that 99.5% of the distribution mass falls below this value. In other words, 0.05% of the mass falls above this value. We will take this value from above and below the distribution, which will result in 99% if the distribution falls between them. Here is the 99% interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5758293035489004\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(73.7773381773405, 74.22325839771896)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "z = stats.norm.ppf(.995)\n",
    "print(z)\n",
    "ci = (exp_mu - z * exp_se, exp_mu + z * exp_se)\n",
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(exp_mu - 4*exp_se, exp_mu + 4*exp_se, 100)\n",
    "y = stats.norm.pdf(x, exp_mu, exp_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=1)\n",
    "plt.vlines(ci[0], ymin=0, ymax=1, label=\"99% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Back to our classroom experiment, we can construct the confidence interval for the mean exam score for both the online and face to face students' group"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI for Online: (70.56094429049804, 76.7095818797147)\n",
      "95% for Face to Face: (76.80278229206951, 80.29218687459715)\n"
     ]
    }
   ],
   "source": [
    "def ci(y: pd.Series):\n",
    "    return (y.mean() - 2 * se(y), y.mean() + 2 * se(y))\n",
    "\n",
    "print(\"95% CI for Online:\", ci(online))\n",
    "print(\"95% for Face to Face:\", ci(face_to_face))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we can see is that the 95% CI of the groups don't overlap. The lower end of the CI for Face to Face class is above the upper end of the CI for online classes. This is evidence that our result is not by chance. There is a significant causal decrease in academic performance once you switch from face to face to online classes.\n",
    "\n",
    "As a recap, confidence intervals are a way to place uncertainty around our estimates. The smaller the sample size, the larger the standard error and the wider the confidence interval. Finally, you should always be suspicious of measurements without any uncertainty metric attached to it. Since they are super easy to compute, lack of confidence intervals signals either some bad intentions or simply lack of knowledge, which is equally concerning. \n",
    "\n",
    "![img](data/img/stats-review/ci_xkcd.png)\n",
    "\n",
    "One final word of caution here. Confidence Intervals are trickier to interpret than they look at first. For instance, I **shouldn't** say that this particular 95% confidence interval contains the true population mean with 95% chance. That's because in frequentist statistics, the one that uses confidence intervals, the population mean is regarded as a true population constant. So it either is or isn't in our particular confidence interval. In other words, our particular confidence interval either contains or not the true mean. If it does, the chance of containing it would be 100%, not 95%. If it doesn't, the chance would be 0%. Rather, in confidence intervals, the 95% refers to the frequency that such confidence intervals, computed in many many studies, contain the true mean. 95% is our confidence in the algorithm used to compute the 95% CI, not on the particular interval itself.\n",
    "\n",
    "Now, having said that, as an Economist (statisticians, please look away now), I think this purism is not very useful. In practice, you will see people saying that the particular confidence interval contains the true mean 95% of the time. Although wrong, this is not very harmful, as it still places a precise degree of uncertainty in our estimates. Moreover, if we switch to Bayesian statistics and use probable intervals instead of confidence intervals, we would be able to say that the interval contains the distribution mean 95% of the time. Also, from what I've seen in practice, with decent sample sizes, bayesian probability intervals are more similar to confidence intervals than both bayesian and frequentists would like to admit. So, if my word counts for anything, feel free to say whatever you want about your confidence interval. I don't care if you say they contain the true mean 95% of the time. Just, please, never forget to place them around your estimates, otherwise you will look silly. \n",
    "\n",
    "\n",
    "## Hypothesis Testing\n",
    "\n",
    "Another way to incorporate uncertainty is to state a hypothesis test: is the difference in means statistically different from zero (or any other value)? To do so, we will recall that the sum or difference of 2 normal distributions is also a normal distribution. The resulting mean will be the sum or difference between the two distribution, while the variance will always be the sum of the variance:\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) - N(\\mu_2, \\sigma_2^2) = N(\\mu_1 - \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "$\n",
    "N(\\mu_1, \\sigma_1^2) + N(\\mu_2, \\sigma_2^2) = N(\\mu_1 + \\mu_2, \\sigma_1^2 + \\sigma_2^2)\n",
    "$\n",
    "\n",
    "If you don't recall, its OK. We can always use code and simulated data to check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZ8AAAD1CAYAAACP+vgcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOydeXiURbb/v/W+by/ZVwIhYSfsq7IJCCqooCDquODoVe84etVxlqvO3PE64zrLnd91meXqjDrqOIMj4y4oiguL7CAB2SEBAoRAyEL2pPtd6vdHku6ut5d0d7o76eR8noeH1Hmr6q1+0+nTdc6pcxjnHARBEAQRS6SuXgBBEATR+yDlQxAEQcQcUj4EQRBEzCHlQxAEQcQcUj4EQRBEzFG6egG1tbUUbkcQBNHDSUtLY55t2vkQBEEQMYeUD0EQBBFzup3yKSoq6uoldFvo2QSGnk9g6PkEhp5PYCL9fLqd8iEIgiB6PqR8CIIgiJjT5dFu/uCco6GhAYZhdPVSug12ux21tbVdvYxuS6SejyRJSE5OBmOs484EQYRFt1U+DQ0NsNlssFqtXb2UboPNZoPdbu/qZXRbIvV8nE4nGhoakJKSEoFVEQThi25rdjMMgxQP0SVYrVbacRNElOm2Ox+CIOIP3eD4+GQLlhc3QWbAokEJWDzIjiRLt/2eS3QRpHwIgogIdU4DS7+swuZyp0v28ckWPPaNhEcnp+LfRiRCIj8a0QZ9HQlAeno6Hn30UVf7T3/6E37729+62i+++CLeeustAMAvf/lLTJ06FTNnzsStt96Kmpoar/lOnjyJuXPnYvbs2ZgxYwZee+0117UlS5b4HEMQ8cLTO+sExdPOuWYDP95cgxu/qEJ1i94FKyO6I3Gz80l//XRE56v597wO+9hsNqxcuRIPPvggsrKyhGuapmHZsmX4+uuvAQCXXnopHn/8cSiKgscffxzPP/88nnzySWFMv3798Pnnn8Nms6GhoQEXXXQRFi5ciNzcXNx8883461//iocffjhyL5IgYsTxOg2vH24M2Oer0w7M/7gCXy3OQYaNvvf2dugdEABFUXDnnXfixRdf9Lr29ddfY+LEiVCUVv192WWXuX6eMmUKysrKvMZYrVbYbDYArRFVniXMr7rqKrz33nvReBkEEXV+u6sOmilF8IIBdiTIopntWL2On2w+L7z3id4JKZ8O+P73v4+3337b6/zI1q1bMWnSJJ9jli1bhvnz5/u8VlpaipkzZ2Ls2LH48Y9/jNzcXACtJj6Hw4Hq6urIvgCCiDI1DgPvH28WZC/PycDy+VnYfn0OpueIUasflbTg7WNif6L3QcqnA1JTU7F06VK89NJLgry8vBzZ2dle/Z955hkoioKbbrrJ53z5+fnYvHkzCgsL8dZbb+HcuXOua3369MGZM2ci+wIIIsqsLm0Rdj3DUmXcMDQBADAgWcFHV2ZjYpZFGPOrwjpoBu1+ejNx4/MJxkcTLe6//37MmTMHt956q0tmt9vR0tIi9PvnP/+J1atX46OPPurwdHxubi5GjRqFLVu2YMmSJQCAlpYWJCQkRP4FEEQU+fiEuItZMjhBiGqzKwwvz8nAnBXn4GiLNzjVoGPVyRZcM5je770V2vkEQUZGBq677josW7bMJRs5ciSOHz/uan/55Zf4wx/+gLfeeguJiYkueVlZGa655hoAwOnTp9Hc3PqHWlNTg23btmH48OEAWtMJnTt3DgMHDozFSyKIiNCscXx12iHIFg30Vigj0y24aWiiIPvLgYaoro3o3pDyCZIHHngAVVVVrvb8+fOxadMmV/unP/0pGhoacO2112L27Nn4z//8TwCt5rn2QIQjR45g3rx5mDVrFq666ir88Ic/xNixYwEAu3fvxpQpU1x9CSIeWFvWgiYPm1teoozJ2Raffe8dkyy0N5c7sb9ajer6iO4LfdIF4PRpd3h3Tk6O4I8ZOHAgMjMzcfToUQwbNgy7du3yOceOHTvw/e9/H0BrOPbmzZt99lu+fLmrH0HEC1+UiqbnqwbZ/Zqcx2ZacHE/KzacdZ8Fev94E8ZmpkV1jUT3hHY+neCJJ57A2bNnA/a55557cNVVV3U415gxYzB37txILY0gog7nHF+aTG5X5gdO7HprQZLQ/uB4M4Vd91JI+XSCgoICzJo1KyJz3XHHHRGZhyBiRXGdhlMN7owFdhmY1c8WcMzCgXZYPT51jtXr2EOmt14JKR+CIMLCHGgws68NCUrgKM80q4R5eeLu6IPjdOanN0LKhyCIsPjK5O+Z14HJrZ3rhojRcJ+cbPHTk+jJkPIhCCJkmjQDG86KO595eYFNbu0sGGCH5wapqFbD0Votkssj4gBSPgRBhMy6Mgc8E1QPSJYxMi244NlUq+TlG1pdSruf3kZQyocxtoAxdpgxVswY+7mP63MYY4WMMY0xdoOHfBJjbAtjbD9jbA9j7OZILj7ahFJS4cMPP8SMGTOQkZHhN+y6nbq6OowePRo//elPXTIqqUDEE5+aTGULBvgPsfbFlQNEE93qU6R8ehsdflVhjMkAXgBwOYBSADsYYys45wc8up0EcCcAcz2AJgC3c86LGGP9AexkjK3mnIf8KZt8xyWhDglIwxvrOuwTSkmF0aNH4x//+Ad+8pOfdDjvr3/9a68oOSqpQMQLBudeO5WrBgTn72lnwQA7/nu7O1nvprMO1DoNpFnJGNNbCOY3PQ1AMef8GOfcCWA5gCWeHTjnJZzzPQAMk/wI57yo7ecyAOcA9InIymNAKCUVRo4ciYKCgg7n3L17NyoqKnDppZcKciqpQMQLhZUqzjW7/9RTLKzDEGszQ1MVFHiY6TQOrDVFzxE9m2CUTx6AUx7t0jZZSDDGpgGwAjga6tiuJJySCv4wDAOPPvoonnrqKa9rVFKBiBdWloih0fPy7LDKoZfHXmDaLX12ikKuexPBeAh9vatCOpLMGMsF8A8Ad3DODX/9ioqKXP/b7XZX4TUASPY3KEzMGal9wTmH1WrFDTfcgBdeeAF2ux2apqGlpQVlZWUYOnSo1zyGYcDhcPic/9VXX8Wll16K7OxsqKrqmqudrKwsnDhxQkhMGs66ezORej51dXVCuYueQvvfWLhwDrxbbIfn99YLrTUoKqryP8gPY5kEwK2APjvRhENHqhCGHosYnX0+PZ1Qn08ga1AwyqcUwACPdj4A7zKdfmCMpQL4BMAvOOdbA/UtKChAUVERCgoKUFtbC7vd/cYMxkcTCsFYqBljsNvt+NGPfuQqqaAoCux2O5KSkqDrurBGAJAkCTabzUsOtJrctmzZgjfeeAONjY1QVRVpaWl44oknALRWN01LS/M5Fmj9YPV3jYjs80lNTcWAAQM67hhHtP9tdYY9VU6cbqlwta0ScMfUwUgNw1cz2OD4r8NnUOts/S5bozHUpQ/EtJzQTHiRIhLPpycT6ecTzDtmB4ACxtgQxpgVwFIAK4KZvK3/BwD+zjl/J/xldi3BlFTwh2dJhVdeeQX79u3D3r178fTTT2Pp0qUuxUMlFYh4YEWJuLO8LM8eluIBAIvEMD/PbHqjnX1vocN3DedcA/AAgNUADgJ4m3O+nzH2FGPsGgBgjE1ljJUCuBHAS4yx/W3DbwIwB8CdjLHdbf9Cc5R0EzoqqbBy5UqMGTMGO3bswE033YTrr78egFhSIRBUUoGIB1b4KBzXGcwh12so6KDXENQnHed8FYBVJtljHj/vQKs5zjxuGYBlZnm8EEpJhcWLF2Px4sVec3iWVPDk1ltvFSqjUkkFortzrE7DEY9MBAoDFoYYYm3mMlNWhG+rVNQ4DKTbKOS6p0O/4U5AJRWI3oTZJHZRX2unlUS2XcaYDPd3YA5g41na/fQGSPl0AiqpQPQmzMpngY9y2eEwJ1fc/Xx9hpRPb4CUD0EQHVLrNLDZtCPprMmtHbPy2UDKp1dAyocgiA5ZV+aA5nG6ryBNwdDUyATHzOxrg+RxtudgjYZzzbr/AUSPgJQPQRAdYvbDXJ4fubM46TYJE7Msgmz7OWfE5ie6J6R8CILokE0m5XNxiLncOmJaH6vQ/qaClE9Ph5RPAEIpqeDZJz09XTgT1M7OnTsxe/ZszJ49G7NmzcLKlSsBtGY2WLhwITQttIJaGzZsQHp6Oj799FOX7Oabb8aGDRtc7dtvvx0lJSUAgKeffhpjx45FXl7HqfkKCwuRmZmJjz76CABQWVmJ73znOyGtzx/33XcfRo8eDYej9QOtqqoK48ePd10/e/Ysbr7Zd/WNUEpXtDN+/HjMnDkTs2fPxiWXXOKS/+IXv8D69evDfyG9hKoWHQfOu9+bDMBFfSOrfKbmkPLpbcTNicbGNQsiOl/SZZ912CeUkgoAUFpairVr1yI/3+vIE4DWsgvr1q2Doig4e/YsZs+ejYULF8JqtWLu3Ll4//33cdNNN4X0OvLy8vDss89i4cKFXtcOHjwIXdcxePBgAMCCBQtw991348ILLww4p67rePzxxzFv3jyXLDs7G3379sXWrVsxY8aMkNboC1mWsWzZMtx1111e11544QXcfvvtPseFUrrCk5UrV3r9Du+55x78+Mc/phD3Dth0VlQE4zMtET+HM8W089ldqUI3OGSpCxO9EVGFdj4BCKWkAgD893//N5588km/RbUSExNd/VtaWoR+V199Nd55J/QMROPGjUNqairWrl3rde2dd94RzhhNnToV/fr163DOl156Cddccw2ys7MFebhr9MW9996LF1980edub8WKFZg/f77PccGWrgiGgQMHorq6GuXl5RGZr6diNrnNzrX66Rk+g5JlZHkotAaN41ANldbuyZDy6YBgSyqsWrUKubm5gvnIF9988w1mzJiBWbNm4bnnnnMpozFjxqCwsDCsNT788MP43//9Xy95OGUfysrK8PHHH+N73/ue17XJkydjy5YtXvL6+nqXOdH879ChQz7vM2DAAMyYMQPLly8X5CUlJUhPTxcymncWxhiuu+46zJ07F3/729+EaxMnTsTWrQHz3fZ6tpSLO59ZETa5Aa2/oylkeutVxI3ZratITU3F0qVL8dJLLyEhwX2orry8HCNHjgQANDU14dlnn8X777/f4XxTpkzB1q1bcfjwYdx33324/PLLYbfbIcsyrFYr6uvrkZKSEtIaZ86cCQDYvHmzIC8vL/favXTEI488gieffBKyLHtd69Onj5BiqJ2UlBRs3LgxpPsAwEMPPYRbbrkFV155ZafW3BGrV69Gbm4uKioqcO211wqHg/v06dNhloreTLPGceC8Kshm9I38zgcApmRbhHLa31Q4ccfIpKjci+h64kb5BOOjiRb333+/q6RCO3a73VU75vjx4zhx4gRmz54NoHX3MHfuXHz11Vfo27evzzlHjhyJxMREHDx4EJMnTwYAOBwOr5IAr7zyCt544w0AwLJly1z+GzMPP/wwnn32WcEM6LnGYNm1a5dr11NdXY0vvvgCsixj0aJFaGlpERRwO/X19T59TgDw17/+FaNGjfJ5bejQoRg/fjw++OADv2u+//77sWfPHuTm5oZt8svNzQXQqmgWLVqEwsJCl/Lx95qIVvZVq8L5nkHJMrLs3l9MIsGFJr/P3mrVT0+iJxA3yqcr8Syp0K6APEsqjB07FsXFxa7+48ePx7p165CVlYWdO3fi5ZdfxksvvYSSkhLk5+dDURScPHkSxcXFrhIK1dXVyM7OhsUinne4++67cffddwMIXCjtsssuw69//WvhW3z7GgcNGhTw9a1cuRKFhYV4/PHHsWfPHpf8vvvuw4IFC7Bo0SIAwNGjRzF69Giv8eHufIDW3Y9nkMXw4cNx8uRJV9uXv80XZWVluOeee/Dxxx8L8sbGRhiGgZSUFDQ2NmLt2rX42c9+5rpeXFyMa6+9Nqy19wYKK0XT1+Ts6Ox6AGBcpvjeP1SjQjM4FAo66JGQzydIOiqp4I/S0lLXN+utW7e6fCG33XYbnnnmGVcE1oYNG3D55Zd3ao0PPfSQkIn7iiuuEJTCY489hjFjxqCpqQljxoxxhY2XlJQEZerbsGEDrrjiik6t0czo0aMxceJEVzspKQlDhgzBsWPHfPYPtXRFRUUFFixYgFmzZmHevHm44oorXMEMqqri+PHjrp0n4c0uk/K5INvip2fnyUmQkZPg/khq0YGjdRR00FNhnIdUETvi1NbWCgvwrGSalpbWVcsKiltvvRVPPfUUhg0b5rfPL3/5S9x8880YN25cwLluu+02PP744wEjuUKt1Nnc3IzFixdj9erVPn047dxzzz34zW9+06GvZeHChXjrrbeQnp4e9BrCYeXKlfj222/xi1/8IugxL7/8Mvr27YslS5ZE5D7x8P4LlXAqUU5/vxyHPcoorFyQjYtzo1dp9LrVlVhb5o6ue3VuBr4z1H9Z+UhClUwD09nnk5aWJmxhyezWCdpLKgRSPk8//XSH8zidTlx99dURf+MnJCTgkUceQVlZWcCS0C+//HKHc1VWVuIHP/hB1BUPACxevBjnz58Pacw999wTsn9L13U88MADIY3pTdSrhlC/hwFeaXAizbhMi6B89p9XEZmjzUR3g5RPJygoKIiIwrBarbjlllsisCJvPA+Kdobs7GyX7ycW+DtkGknI1xOYb6tUeJolCtKUsEtmB4vZ77OPgg56LOTzIQjCJ2Z/z6Qo+nvaGZtByqe30G2VjyRJcDrpkBkRe5xOJySp2/5pxIxdleIH/wVRjHRrZ0SaAovHoy9rMlDdQuUVeiLd1uyWnJyMhoYGNDc3d/VSug11dXVITU3t6mV0WyL1fCRJQnJycgRWFN94hVlH2d8DAFaZYUSagv0eiUwP1WiY2S86Z4uIrqPbKh/GWMgn/Xs6586dCxg40Nuh5xM5zjsMlNS7dxwyA8bHQPkAwOgMi6B8DtdomBnhEg5E10O2BYIgvDD7e0alK0hUYvNxMTJN/E58qIb8Pj0RUj4EQXjRFf6edkamizssz3NGRM8hKOXDGFvAGDvMGCtmjP3cx/U5jLFCxpjGGLvBdO0OxlhR2787IrVwgiCih3nnE820OmZGpYs7n8O08+mRdKh8GGMygBcALAQwBsAtjLExpm4nAdwJ4J+msZkAHgcwHcA0AI8zxjI6v2yCIKLJHlOI8+QYhFm3MyRVjHg702SgxmHE7P5EbAhm5zMNQDHn/Bjn3AlgOQAhhwnnvIRzvgeA+R1yJYAvOOfVnPPzAL4AENmSpARBRIa2VFu1TgMnG8Rgg9HpsVM+FolheCrtfno6wUS75QE45dEuRetOJhh8jc3z17moqEj4n/CGnk1g6PkExvx8rOcrkLP1cySVHoXt/DlwJuHcgHGYnzgPX2aMAxjDwAQDp44X+5kxOuQpVhz0+Hj6+shpZNZF/7wPvX8CE+rzCZQBJhjl4yufebDZSEMaW1BQQMn9AkDPJjD0fAIjPB9HM6zvvw7Llx+AaeKuYmjxDnyGHViZdQG+O+YBXNgvHQUFsQ1hv7ChDl9W1rva522ZKCiIbl5Bev8EJtLPJxizWykAz3dePoCyIOfvzFiCIKIAKy9FwlM/gPWzt70UjyeLqwrx0d5nMSk59hkGvIMOKOKtpxGM8tkBoIAxNoQxZgWwFMCKIOdfDeAKxlhGW6DBFW0ygiC6AHnvDiQ+8R+QS33XSzJzWc1+fG/VbwEjtg5/r3BrUj49jg6VD+dcA/AAWpXGQQBvc873M8aeYoxdAwCMsamMsVIANwJ4iTG2v21sNYCn0arAdgB4qk1GEESMydy1Afbn/gusqVGQG5k5aLnzITT+/l00/Nfz2Jcsmthyigth+erDWC4Vw1IVyB5G+9JGHXVOinjrSQSVXodzvgrAKpPsMY+fd6DVpOZr7GsAXuvEGgmC6Aycw/r+axj0yT+8LqnTL4Xjez8F7K0F2w6zNCyc+Cg++/Z/cEFDiauf9d1XoE2eCZ7dLyZLtskMQ1MVFHkcMC2q1XBhn9idNyKiC2U4IIiejKbC9vJvYV0hKh7OGBxL74PjvsdcigdoLWFQbUnBteMfQq2c4JKzlmbY3njeFY4dCyjNTs+GlA9B9FQMHfa//AqWzZ8LYm6xouWBJ6EuvBlgYkBqe/2cMlsmfj5MLHCo7NkG+UBhdNfswSjy+/RoSPkQRE+Ec9j+/nsoO9aL4pQ0NP/8eehT5vgc5lm87a+5l+LMwHHCdeuHf4vZ7mckpdnp0ZDyIYgeiOXTf8GydqUgc2T0QdMvX4AxfKzfcfvOuz/gOZNQdf09wnX5yN6Y7X7MyucQ7Xx6FKR8CKKHwcpOwPr+q4LMyOyDotseAu/rMy4IAFDVouNMkzuizCIB/SeMhzZBTGhi/eD1mOx+CtIswin1kw06GlWKeOspkPIhiJ6EYcD++jNgqscOJikFzT99BmpaVsCh+0zJREemW2CVGZzX3inI5aJ9kIr2RWzJ/khQGAanuCuYckCIfiPiG1I+BNGDUNathHxkryBz/NtPwPsP6nDsXpPyGZfRavYyho323v2sfqeTKw0Oqu3TcyHlQxA9BdUJ60d/F0TaxBnQZlwW1HDzzmdcpvuDX114s3BN3rkRrOJMmAsNHqrt03Mh5UMQPQRl0+eQaqpcbW61w3HHg17h1P7Yd17cVYz3UD766MnQ84e62owbsHz5QSdX3DHmcGsKOug5kPIhiJ6AocO6arkgUi9ZBJ6VE9Rwp869dhWeOx8wBvVKoUgxLOs/AZqbwltvkNDOp+dCyocgegDyNxsglZe62lyWoS64KejxR2o1eAaS5SZKyLLLQh9txjwYKe6yBqy5EcrWr8JfdBAUmLIcHK/X0aLFLssCET1I+RBED8C6+l2hrV10edC7HsCHvyfDR+VSqw3aJYsEkWXtiqiGXSdZJAxMditBgwPFdWR66wmQ8iGIOIedOQm5WAx9dl59i5/evgkUbOCJeskicA8fknyiCNLxwyHdK1TI9NYzIeVDEHGOZcNnQlsfOTGo0GpPPDMbAP6VD8/uB90Udm1ZG2x5r/Awh1tT0EHPgJQPQcQzhg5lk5g4VJ29IKQpOOdB73wAQL3sGqGtbP0KaKz307vzUI63ngkpH4KIY+R930CqqXS1uc0ObdrckOYobzZQ2eKONrDLrcXc/KFPmA4j0+1PYk4HLJu/COmeoUDZrXsmpHwIIo5RTCY3beolQn2eYDDvekZnWKBIAc4GSTJUU+CBsiZ6gQcjTBFvR+s0OHWKeIt3SPkQRLzSUAelcKMgUi9eGPI0QUW6mdDmXg0uuT8+5LISSKa0PpEi1SohL9Ed8aZx4Fg97X7iHVI+BBGnKNvWgGluxWHk9IcxckLI8wQbbOAJT8+CfsFsQRbNwANvvw8pn3iHlA9BxCmWDZ8KbXX2gqBT6XgSSrCBcD9z4MGO9UBdTcj3Dwbv2j4UdBDvkPIhiDhEKj0G2eN8DWcM2uwrQ56nReNeZQrGBmF2AwB99AUw+ua52kxTYdn4WYAR4UNBBz0PUj4EEYeYAw30MReAZ/UNeZ5DNSo8ffcDkmWk24L8WJAkqJcsFkSWtSsAI/IF37x2Pudp5xPvBPUuY4wtYIwdZowVM8Z+7uO6jTH2r7br2xhjg9vkFsbYG4yxvYyxg4yxRyK7fILohWia19keLYxAA8BXDZ/gdj3tqBcvAFfcY6RzZVEps20+aFpUp0EzKOItnulQ+TDGZAAvAFgIYAyAWxhjY0zd7gJwnnM+HMDzAH7XJr8RgI1zPh7AhQD+o10xEQQRHvLuLZDq3b4VnpgE7cKLw5orXH+Pi5R0aFPFc0XRCDzIsEnom+D+uFIN4DhFvMU1wex8pgEo5pwf45w7ASwHsMTUZwmAN9p+fhfAPMYYQ2vl2yTGmAIgAYATQF1EVk4QvRTLhlVCW5sxH7DawpornEg3M+bAA7lwI5hHXaFIQWl2ehbBKJ88AKc82qVtMp99OOcagFoAWWhVRI0AzgA4CeAZznl1J9dMEL0Wdr4S8rfbBJk6JzyTm6+0OhPCUD5GwXjoeYPdazQMKJtWh7WmQFC4dc/Cfw4NN75iN83GVn99pgHQAfQHkAFgA2PsS875MV83KioqEv4nvKFnE5ge8XwMJyxqGRT1DCxaOQBAU7Kgy9lI31WEJO526Dfn5OOwKgFBvm7P53O2haHWmeBqJ8oczrPHUVQe+pL7jJmO/NMlrjb/8iMUFUwJK/TbH5lOBYDV1d5xqhpFiWcjNj/QQ94/USTU51NQUOD3WjDKpxTAAI92PoAyP31K20xsaQCqAXwXwGeccxXAOcbYJgBTAPhUPgUFBSgqKgq44N4MPZvAxPPz4c4aaJXboFdugV69CzAcvjv2BxomKUjcp0HSAOnya1EwYkRQ9zA/n+KTzWj9M21lfJYNI0fkh/cC+vUBX/MemN66G7FXl2MkWmAUhH7o1R8Xpzjwu6PuPHZlegIKCkLL3h2IeH7/xIJIP59glM8OAAWMsSEATgNYilal4skKAHcA2ALgBgBrOOecMXYSwGWMsWUAEgHMAPD7SC2eIOIVzg0YDcehVxdCr9wCo/YgvA0KPpCBxokKmkfISN5pQL9ofthr6HSwgScp6dAvmNV60LQNy/pVcIyInPIx1/UpqlWhGxxyoDx0RLelQ+XDOdcYYw8AWA1ABvAa53w/Y+wpAN9wzlcAeBXAPxhjxWj9KrW0bfgLAF4HsA+tprnXOed7ovA6CKLbw3UH9Kod0Co2tu5u1Nqw5zISGOpmy7DWrIMl5dqw5vAKNggxzNqMOucqQfko29fBcduPgITQEp36I9suI8smocrRanZs0YGTDTqGBMjATXRfgvqtcc5XAVhlkj3m8XMLWsOqzeMafMkJojdhOKqgHn8TWvkaQG8JagyzZUNKHQEpaRDAFPCGU9BPrQO3i/2cRX8BmARL/jW+JwpARHc+APRxU2Bk9oFUXQEAYM4WKNvWeJXe7gyjMhRsOut0tQ/VqKR84hT6rRFElOC6E+qp96GeWB6U0pGSh0HOngG5z0xIyUPBPJz1yvpPYH3vMzSNU9A4TgZk9zXnkRcByQJL/+Cj3hpVA8fqdFebARiT0cmPA0mGNnsBrCv+4RJZNnwaWeWTbhGUz+EaDQsHRmx6Ilv3Dj4AACAASURBVIaQ8iGIKGA4quD49jEYDUf9d5ITIWdMhJw5GXLWdEgJ/tPjWDZ8CkkDkndrsJwzUDPfDjB31Jvz8IuQUkZCThka1Pr2VauCh2loqowkS+ezbakXLxSUj1y8H6zsRMhlvf0xMo0SjPYUKLcbQUQYo6EELd/8xKfiYdYsKPlLYL/gGSRe/A7sEx6HJf+agIqHlZ+GXLTP1baVGbAP+hHAPMxkXIXjwO/AdT9Rcib2eJ3vsfrpGRo8pz+00ZMFmeXrVX56h475oOnhWjrrE6+Q8iGICKLX7EPzzgfBHRXiBSUF1hH3I2HmG7CNuA9y+jgwSfY9iQnFVKJaLxgHefgC2MY8LMh54wk4j74W1JzmnG4Tsjrn7/FEm3OV0FY2fQ5okVES5oi3IzUajChVUCWiCykfgogQRuMJtOx5AtCbBLmcPR2JF70GS/41YFKIlm7OYdksJhFVZ7WWTlD6zoXSTwy11ko/gla1s8Np91RFUflMmQOemORqS3XnIe/veE3BkJMgId3q9nc1ahyljXqAEUR3hZQPQUQAw1GFlt2/BLQGQa7kLYJt/GNglpSw5pWK90M65z7TzRULtGmXuNrWEfeB2UWTnfPIC+CGE/5QDY4DpjDr8Z2MdBOw2qBNvVQQKdvWRGRqxhjV9ukhkPIhiE7CtWY4vn0M3HFOkFuG3AbriB+gNTF8eFhMpRP0SRcBSW5FxpQk2Mb8DJ5/yry5DOqpD/3OebhGg9Oj5E6/BAk5CeGv0RfajMuEtlK4EXAG54/qCKpq2jMg5UMQncR55P+8gguU/lfBMvhWIVw6ZAwd8s4Ngqjd5OaJnD4WSp7oZ1FL3oLh8J1Zek+VuCuKpMmtHX3URBhpGa42a26EvHd7ROb2CjqgnU9cQsqHIDqBeuZLaGe/EmRy1vS2HU/n0r5IxQcg1Z13tbk9Efr4qT77WofeDijJboHeDNVP8EG0It0EJBna1EsEUaRMb+agg8O084lLSPkQRJgYjafgPPJ/gowlDYJt3CNBR7IFQjHterSJMwCLb0XBLKmtCsiz/9mvoNce8OprDjYYH4WdDwBo002mt11bAEdzp+f1tfPhFPEWd5DyIYgw4IYGx/7/ETMXSDbYxz4CJtv9Dwz6BrzVT+KB3kG1UqX/1WBJgwWZ88ifwT1KMBg+avhMjJLyMYaPhZHZx9VmzhYou7d0et7+iRJSLO5dZZ3KcabJCDCC6I6Q8iGIMNBKP/Ty81hH3AspeXBE5pdKj3tHuU2YFnAMk2TYRtwnyIz6Imhn3EELJ+p11KnuXUKqlWFQcmSDDVxIErRppqi3rZ03vTHGfBSWI9NbvEHKhyBCxGipgPP4MkEm58yBkrsgYveQzbuesRcCCUl+enuMy5gIOUfcITmPvg6utoaAm/094zMtnfZNBcJsepP3bgOaGvz0Dh4qqR3/kPIhiBBxFr8imtuUZNhG3B/RD3Fl12ahrV0wO+ix1mHfByQP35BaC2fJmwB8RLpF8nyPD4whI2H06e9qM1WFUrip0/OOSqOdT7xDyocgQkCvLoR+7mtBZh16J5g1PXI3aayHVHJYvO+ki4IeLiX0hWXQTYJMK10BRT3jI7NBFCLdPGEM2vTIHzilHG/xDykfgggSzg04il4WZFJKAZS84EsZBIN8oBDMI3pLzx8Knp4V0hyWgTeA2XLcAq4j7fw72FMd250P4MP0tv8boCH8QnqA90HTg+dViniLM0j5EESQ6BUbwRtLPCQM1pEPdCqDgS8UUx40feyFIc/BZDusBfcIMpujCNPZVndbBkakR7+qijFgKAyPkgpM1zttehuQLCNRcZs5a5wcFS0U8RZPkPIhiCDg3IDz+D8Fmdz3EsipIyN+L3n/N0JbHzslvHn6zIKceYEgeyzjbSSx1rM2YzIssEjRCzZwwZj3gdPt6zo1pcQYRnjV9iHTWzxByocggkCv2Gza9UiwDv5uxO/DKs6IIdayAn3UhPDmYgzWEfcDzP0hnavU4D/TVgKIjcmtHW3aXKEtH9gJNNR1ak5fpjcifiDlQxAd0LrrMYVW950LKWlAxO9lLj1gFIwFbAlhzycl5sMy8HpB9v3UL1FgKYtKTjd/GHlDYOS6611HwvQ2NkNcv/nwLNG9IeVDEB2gV27x9vUMviUq95L3iSY3LUyTmyeWwd8Fs7kzDViYjl9lvIkJGbFTPmBMKAUBAMqOdZ2a0lwGwlwgj+jekPIhiA5QT74ntOWcOZCSBvrp3QkMA8qBQkEUTrCBGSbboQ25W5DNTjiEMfpmPyOig9nvI+/fCTTWhz3fOJPyOVijQjUo4i1eCEr5MMYWMMYOM8aKGWM/93Hdxhj7V9v1bYyxwR7XJjDGtjDG9jPG9jLGIpD4iiBig15fDMOUnDNaux7pRBFYo9sPwhOTYAyJTEDDXjYNXzePEWTs2F/BtSY/IyKPkT8ERq7bVMl0Dcqu8E1vfRJk5Ca6P8IcOlBE533ihg6VD2uNI30BwEIAYwDcwhgbY+p2F4DznPPhAJ4H8Lu2sQqAZQDu5ZyPBXAJANobE3GDVrpCaEsZkyKWv82MfMAUYj36AiAC2bEBYE+1hl9UfxdO7p6PO6vgPP5mROYPiihEvZHpLX4JZuczDUAx5/wY59wJYDmAJaY+SwC80fbzuwDmsdZcI1cA2MM5/xYAOOdVnHMquE7EBdxZC618rSCz5Jvf+pEjGv6edvZUqziq5eLluivEe5R+AL3+WMTu0xHaVFPU275vOmV681I+VaR84oVglE8egFMe7dI2mc8+nHMNQC2ALAAjAHDG2GrGWCFj7GedXzJBxAa17DPAcH+YMXtfyNmBM0uHjdMBuWivIIqEv6ed9h3B72sXo1TLdF/gBpyH/yiUXYgmxoBhMPrmu9qtprfwfU/jTYXwaOcTPwRzvNnXKTSzV89fHwXAbABTATQB+IoxtpNz/pWP/igqKhL+J7yhZxOYiD0friPnzIfCH0iN7SKcLo7OLiHl2AEMV90fnI60LBypawLqO/96nAZw8HwCAIZmbsMvqm/F33L+5Lpu1B1C2e430JQcfPLSzpA7fAL6lZe62o51n+BY36FhzZXSzAC4Q9F3VbTgyJEihJvjlf6+AhPq8ykoKPB7LRjlUwrA80BDPoAyP31K2/w8aQCq2+TrOeeVAMAYWwXgAgA+lU9BQQGKiooCLrg3Q88mMJF8Ptq5jXCUuktYQ7Ihd8KtYJaUiMxvxloo/klIk2agYMSIiMy9u9IJnVe42gelCyFnz4Re6d5xpNd/gv5jr4tsglQ/SNbrgE2rXO3U4wdRkJcLJCYHGOWbYZwjdc8ZV42iOo1B6TcEQ1NDTxtEf1+BifTzCcbstgNAAWNsCGPMCmApgBWmPisA3NH28w0A1vDWLH+rAUxgjCW2KaW5ALzr+hJEN0Mt/UhoK/0ui5riAbwPl0bS5Gau4TMhywLriPsAz4qrWgOcx95ALDAGDofR1225Z5oatulNYgyTskXT284Kp5/eRHeiQ+XT5sN5AK2K5CCAtznn+xljTzHGrmnr9iqALMZYMYAHAfy8bex5AM+hVYHtBlDIOf8k8i+DICKH0XAMRo3of7HkX+OndwSoq4F8QjRnaGMu8NM5dMxO+AmZFkj2PrAOuU28Z9ln0CNg5usQX1FvO9aHPd2UPmLQwc5KUj7xQFB7U875KgCrTLLHPH5uAXCjn7HL0BpuTRBxgXrKFF6dPgFS8pCo3U85aDpYOqgASImc+cvXzgcAlPwlUMs+A29q979wOI/8GfYLno1qdVMA0KZdAuvH7jBved92oLkxqGqtZi4w7XwKKyjoIB6gDAcE4QFX632EV0dx1wPvEOtws1j7Qje4V86z9oSiTLLAWnCvcM2oPQDd9PqjgTFwOIwcU4XTME1vF/YRlc+31U7KdBAHkPIhCA9aw6sdrjaz5UDODr6KaMhw7u3vGRc5f8+xeg2NmvuDOMPGkJfkPmiqZE2BnD1dGOM8+hq47kBU8Wl6WxfWVLmJMvqbMh3sp5Drbg8pH4Jog3Md2umPBZmSvwgsQlkGfMHKT0OqKnevwWKBXjA+YvN7lc3OtHqZ1KzD/wNgbr8Jd1RCLTXHFEUec6JRee92oDm8dD9m0xv5fbo/pHwIog29cht4i1sRQLLC0n9BVO/pVThuxATAaovY/F7Kx0cZBSmxP5T8xYJMPbEcXO1cvZ2OMAYVwOgjmt7kfdvDmstsettJfp9uDykfgmjD/G1f6XspmCU1qvdUvPw9kTO5AT6CDfwUkLMOXgooHs5+rRHOkuURXYsXjEG7UDzYqhSG5/fxCjqgnU+3h5QPQQAwGkpgnN8tyJQo5nEDAKjOiJXM9gXnPKidDwAwSyosg5YKMq10JYzmsxFbjy+0ybOEtvLtVkAPPTP1pGyLkGblcI2GOmdsUgYR4UHKhyDgveuR0sZBTgkv5UuwyIf3gDlaXG0jPQvGwOERm7+syUCVw/0BbJc4hgc4+W/JvwbMlu0WcBXOY3+P2Hp8YRSMBU9y7y5ZYx2kon0hz5NmlTAizf3aOIDdlGS0W0PKh+j1cLUe2lkxvY1lQHTDqwFA3r1FaOsTZwBS5P4k91SJpqeCJAOy5P/8DpNtsAy9XVxT+Vro9UcjtiYvZAXaJDGaMNzy2ma/TyFlOujWkPIhej3amc9N4dXZkLNnRvemnEPZLfo3zB/CncXs7xmR1LEZSuk3DyxpsIeEQz36akTXZUabLD5rZdcmgId+TudCynQQV5DyIXo1nOtQS1cKMiVvEZgUemLKUGBnTkKqOONeh2KBHsGUOgCwq1JUPqOSO1Y+jMmwDr9LkOnVhdCrC/2M6Dz6+KngiltxSOfKIJ0uCXmeC01BBzvOOcHDUGJEbCDlQ/Rq9Kod4C0eTnXJEvXwagBQzCa30ZMAe2JE7/Gtyew2OgjlAwBy5hRI6RMFmbP41ejV/LEneileOYxsB2MzLUiQ3WbFs80GTjZQ7cruCikfoldjzuOm5MyNSVkBcyoZfWJkTW5nmnScaXIrC5sMDEsMbhfAGPPa/RgNR6GXr4vkEgW0C0xRb7s2hjyHRWK4wGR623aOTG/dFVI+RK/FaDwJ47xoTop6eDUAVlMFyVS1NNL+nt0mf8e4DAuUEP7a5dQRkHPEktfOY2+AG9H5MNcniX4f+ehBsJqqkOeZniOa3raT8um2kPIhei3e4dVjIKdGv5iYXLgRzMMXoQ8aAd4nN6L3MIcZTzb5Q4LBOvQOgHmEL7eUQyv9OMCI8OEZ2dCHjBJk5mjAYJieI2aH2ErKp9tCyofolXCtEdrZLwVZtLNXt6N887XQ1qbOifg9zDufSdm+D5cGQkrsDyXvakHmLHkLXG3o1Nr84RX1Vhi66W2aaedz4LxKh027KaR8iF6JVvYZoLsPeDJrJuQ+swOMiBANtZAP7hLXMiWyyodz7rXzmZQV+s4HAKyDbwFkj0AIrR7qibc7szy/6BeIz18+sBNwNIc0R4ZNwkiPw6YGp8qm3RVSPkSvgxsa1FMfCDIl7+qoh1cDrQcomeH+Jq7nDQbPHRjRe5xpMlDe7JHZQAZGpYf32pg1HZZBYp1ItfRDGI7KTq3RF0b+EBjZ/dz3VlWvchPBML2vqGjJ9NY9IeVD9Dr0c1+De354SlZY8hbF5N7mctH61Ll+eobPLpPJbXymBUqAzAYdYRlwHZg1yy0wnFCPv+l/QLgw5m16C8PvYza9UdBB94SUD9Gr4JxDPfmeIFNyrwCzpkX93qzuPOR9OwSZNiXyysfL5BZGsIEnTLbDMuRWQaadWQ2j8VSn5vWFV9Tb7i2AEZrPZoZJ+XxT4YROlU27HaR8iF6FcX43jAbPXGUMlgHXxeTeyra1osktfwiMAZFPXuoVbOAnk3UoKLlXgCXkuQXcgPPYG52e14w+cgK4PcHVlmqrIZ04EtIcw1IVZNncH231Ksf+85RktLtByofoVZh3PXKfmZAS8/z0jizKli+EtnbR/Ijfw1ewQThh1maYpMA67A5BpldshF53uNNzC1is0MdNFUTKrtBMb4wxMr3FAaR8iF6D0VACvVqsn2MZ+J2Y3JuVl0I+elCQRUP5nG7UUdHi3l0lyEwoNdAZ5D6zIaWI56DU48siMrcn5gO34Zz3mWEKOqBMB90PUj5Er0E9+a7QltLGQE4bE5N7K5vFM0X6yIngWX0jfp9dPorHdSbYwBPGJFiH/bsg06t2RHz3o0+cAc7ca5ZPHAGrrghpDvPOhyLeuh9BKR/G2ALG2GHGWDFj7Oc+rtsYY/9qu76NMTbYdH0gY6yBMfZwZJZNEKFhOCqhmXKTxWrXA85h2SIqH3Xm5VG5lflMy8QI+Hs8kTImQ0obK8giHfnGUzNgDB0tyORvt4Y0x+QsK6wen26nGnSUNVKS0e5Eh8qHMSYDeAHAQgBjANzCGDN/XbwLwHnO+XAAzwP4nen68wA+7fxyCSI8tFMrAO4uz8wS+kPOnhGTe0vHD0MqL3W1uWKBFoUQa8DbvGTOddZZGGOwmiLf9KrtEd/9eBWYC9H0ZleY18Fa8vt0L4LZ+UwDUMw5P8Y5dwJYDsCcfXEJgPbQl3cBzGOsdd/MGLsWwDEA+yOzZIIIDa41QS37RJBZBlyP1u9V0UfZLAYa6BOmA0kpEb+PU+deZ3ymRlj5AO27H/H7p3r8nxG9h272+xzYCTgdfnr7xtv0Ftp4IroE44nMA+AZ0F8KYLq/PpxzjTFWCyCLMdYM4L8AXA6gQ5NbUVGR8D/hDT2bwPh6Pkn1a5CmNbraupSEE41DwGPxLA0d4zZ/LohODhmH2ijce3+9hBbd7mr3sRpoKTuOIg+XT6TePzbrJcjCAVdbr9qGkv1fQbVGKFsD5xibmglrXTUAgDkdKP/yY9QVTAh6ioG6DMCdaPTrk3UoygzsO6K/r8CE+nwKCvwn6g1G+fjyVppPbPnr8ySA5znnDYx17PQsKChAUVFRwAX3ZujZBMbX8+G6E81b1gtvWPvAazF8qOi3iBbynm2wNNa715OYhJwF1yHHagswKjy+2N8AoNbVntk/ESNGDHC1I/n+4Xw4WnaugVF3yCXrp2+AveCJiMwPAGzKxcCaj1ztgedOwHFV8H66tHwdPzvkLhR4pFFG3pBhSPRTW4L+vgIT6ecTjNmtFMAAj3Y+gDJ/fRhjCoA0ANVo3SH9P8ZYCYCfAPhvxtgDnVwzQQSNVrYK3FntFkg2WPIXx+z+iinQQJsyF4iC4gFay0Z7Mi0nOvcBWn0/liG3CTK9civ0+uKI3UMzZzv4dgsQQlnsnAQZQ1LcplWNAzsr6LBpdyEY5bMDQAFjbAhjzApgKYAVpj4rALSfQLsBwBreysWc88Gc88EAfg/gN5zz/4vQ2gkiIFx3QD3xL0Gm5C2KSaVSAICjGcrODYJIi1KUG+DtUI90sIEZOfNCSKkjBVkkfT/66EngVrcZUaqugHQ8tMCGGX1FBbylnPw+3YUOlQ/nXAPwAIDVAA4CeJtzvp8x9hRjrL0Ayqto9fEUA3gQgFc4NkHEmtZdz3m3QLLBOuiGmN1fKdwE5nCXbTAysqGPnBiVe5U2aDjd5A4ltsnAhMzIhlmbYYzBMtgU+Va5GXr9scjcwGqDPmGaIFK2rQlpiotMh003l1PEW3chqHM+nPNVnPMRnPNhnPNft8ke45yvaPu5hXN+I+d8OOd8Gufc693HOX+Cc/5MZJdPEL5p3fWIdWcs+YvArBkxW4OXye2i+YAUnXPd5l3P5CwrrHJkDpcGQs6a6p31oCRy5360aZcIbWX7upBMb7NMO58d55xQKclot4AyHBA9ErX0I69dj2Xgjf4HRJq6Gsh7twuiaKTTacd8vsccZhwtfPp+KjbBaCiJyPzaxBngHj4yqfocpKMHAowQGZoqIyfB/THXqHHsqSK/T3eAlA/R4+DOGqglywWZJX9x7Hw9ACzb1ngVjTMGDIva/bZXdI3yAQA5axqklOGCzGnytYWNPRHaRNOB0xBMb4wxzDTtfjaT36dbQMqH6HE4j78J6E1ugZIMy6CbY7oGL5PbzMuBII4bhEOTZmCv6dt8LJUPYwyWQUsFmV6+HkaTOSg2PLTplwptZfv6kGr8ePl9zpLfpztAyofoURiNp6CZshlYB98CZol8RgF/tGawFk1D2ox5UbvfrkoVmocbY0iKjJyE2GRvaEfuMxMsyfOAqeHlcwsXfeIMcJtH1FtNZUjltWf28454M0LwGxHRgZQP0aNwHn0V4O5vxcyeCyWG53oAQNnyldDWR0wAz+4XtfttPiuakaKRUqcjGJNgNe1+tLNfwmgJLRu1T6w2r4qvlvUfBz18TLqCVKt711nj5DhUowUYQcQCUj5Ej8HWfAB6pZj92Dr838GkGH4YxzCDdTsbTWak2f2id7g0EHLOXDB7rlvANagn34nI3Orcq8V7FW4Eq63209u0Lonhohyz6Y38Pl0NKR+iR8ANJ9JqTPV6UkdD7nNxTNchHT8M6aw7FSKXlahlsAZak4maw6zN4cWxgkkyLINvEmRa2Wdi1GGYGCPGw8h1m/WYrkPZuDro8Rd5HTYlv09XQ8qH6BGoJ9+DonmaeBisI+5HMDkFI4m5VLY+cTqQnBq1+xVWOtGsu/0XuYkShqbG1t/jidJvPpgt2y0wnFBPvt/5iRnz2v1Y1n8SdODBzH7mw6YOcPL7dCmkfIi4x2g+6xVareRdDTk1xkkiNc3L3xNtk9smk8ltVj9bzBWuJ0yywDJQzCKhnv4YXK33MyJ41FlXgsvuXMhSeSnkPcEVmZuUZUWCx6HbM00GTjRQcbmuhJQPEddwzuEs+jNgeNjwLWmwDr3D/6AoIe/dDqm+xr22xCTopjMqkWajyXfRVf4eT5T+CwCLx5kqvRlq6Uf+BwRLarqXCdP6yVtBDbXKDFP6iOmGNpHfp0sh5UPENXrFJuiV2wSZddj3Yhpa3Y5l42dCW5t2WdQyWAOAanCvzAaz+8U+0s0Mk+2wDLxekKmnPgTXmvyMCB71KjGiTj6yF1LRvqDGXuQVck1+n66ElA8Rt3CtEc4jLwoyKXU0lNzomrp80lAH2VTqWZ19ZVRvuavSiSaPAz59EyQMSw2mRFf0seRdDSjJboHWAPX0J/4HBIkxqADa2CmCLNjdzyyvw6a08+lKSPkQcYvz6OtCrR4OCbZRPwZjsX9bK9vWgGnuLANG33wYw6NbsM7s75ndxf4eT5iSBEv+EkGmnnwPXO/8B7666LtCW9m1Cex0SYfjpvSxQvF4PMfqdZxtIr9PV0HKh4hL9NoD0EzfpBtS5kNKHtwl67GYwn7VWVdELZ1OO93R3+OJZcC1gJzgFqg10Mo+8z8gSPTRk6EPEesIWVct99PbTZJFwqRs0e9D9X26DlI+RNzBDQ2OQ3+EZzV3ltAf9anRNXP5g5WdgHzsoCDTZl0R1XuqBsfWcnOkW9f7ezxhlpRW85sH6sl3wI1OZpVmDM6rbxFEypYvwarPdTjUnGTUvHskYgcpHyLuUE++C95YIshsI38IxDKTgQeWTZ8LbW3UpKim0wGA3ZUqGj38PTkJEgrSuoe/xxNlwPXC74U7KqGd/SrAiODQL7wYRt98V5vpGiyr3w0wohXzeZ/1Z2jn01WQ8iHiCqOpDGqJWKpZ6TcfcubkLlqQDmWzSflEOdAAANaWtQjtWX27j7/HE8mW2Rp67YFa8i9wo5O51SQZzoVipnLL2hVAQ13AYTP72gS/T1GthpMNlOetKyDlQ8QNnHM4Dv8JMDxMJZZUWIff3WVrkg/uglTtzqzArXavJJjRYM1p8Rv7pXndy9/jiWXgDQBz78p4yxloZZ92el5t1hUw0tyVaZmjBdYv3gs4JtUqeSVeXXuadj9dASkfIm7Qzn4F4/wuQWYdfjeYNa2LVgQoG0xne6bMARISo3rPWqeBHabicfPy7H56dz2SPccr/N15/E1wrblzE1ttUBeYdj+fvwc0NwYcZn5Wa0y7SCI2kPIh4gLurIGz+GVBJmVMgtIveqWpO4LVVEHZvk6QxcLktr7MAY90bhiVriAvqevyuQWDZchtgOSxO1NroJ4KvEsJBvXSa8CT3AeKWVMDLF99GHDMZf3FXeK6Mgc0g/K8xRpSPkRc4Cx+BVA97PmSBbaRP+xSP4dlzQow3e0vMPrmQx8dfd/TmtPiN/XLurHJrR3JlgXLgOsEmXry3c5nvE5IhPMKMZec5bN3AIf/3czELAsybe6Pvlqnd6YIIvqQ8iG6PVrVTq8IKcvgWyEl5nXRigCoTihrV4iiy68HpOj+SXHO8Xmp+MHanU1unlgG3QhYPEykegucx/7e6XnVy68Ht7tNnVJ9TcBic7LEMD9fVNgrT3TSBEiETFB/KYyxBYyxw4yxYsbYz31ctzHG/tV2fRtjbHCb/HLG2E7G2N62/y+L7PKJng7XW+A8/CdBxpIGe2VOjjXK9nWQ6tzf2rk9EersBQFGRIZvq1SUNbnLCCQqzOvsSneFKUmwDhbP52hln0KvCS43m1+SUqDOF3dVlk+WA6r/3cziQQlC++MTLaAKC7GlQ+XDGJMBvABgIYAxAG5hjI0xdbsLwHnO+XAAzwP4XZu8EsBizvl4AHcA+EekFk70DtTjb4K3nPWQMNhG/QRM6sIzLYYOy8diuLc6Z2HUAw0A4JOTJpNbfxsSlO4XYu0PJe9qMNOO1XHoj+BG58xezitvBPdI4irVVELZ6D+bwrw8m1BiobRRx8EGMgTFkmCe9jQAxZzzY5xzJ4DlAJaY+iwB8Ebbz+8CmMcYY5zzXZzzsjb5fgB2xlh8fE0juhy9vtjLKa3kL4acNqqLVtS2hm3rIJeVuNqcSV7fvKPFp6dE5bNwYHyY3NphkgW2kT8WZLzpJNQTnSy3nZoO9dJrBJH1438Cmu8zPImK5GV6+6qyewdt9DSCUT55AE55tEvbZD77a51iwgAAF1pJREFUcM41ALUAskx9vgNgF+ecguqJDuFch/PQHwDuNjExWzasQ+/sukUBgKHD+tHfBJF20Xxwj9P20eJEvYZ91e7UNBIDrhwQX8oHAOSMCVByxahAtWQ5jIaSTs2rLrwZXHHnbpMqz0LZ4P88kdn09mmFTFFvMSQY24WvPb35NxSwD2NsLFpNcQETXhUVFQn/E970lmeTVL8WafXia61MuR6O46cDjov288nYswWDz7i/i3EmoWjSHDhi8Hv5R6kCwH1AckKKjvOnjiGUeLHu8v5h7FLkSJshG20VTrmKusInUNn3YXApfONI/sRZ6LNznastvfcaivsNE5RSOyN1IFFOQJPe+vFV4ZSwbMcxzMoMrjR3byTU909Bgf9qwsEon1IAAzza+QDK/PQpZYwpANIAVAMAYywfwAcAbuecH+1ooUVFRQEX3JvpLc/GaC5H8/ZVgkzOuRgDx13vZ0QrUX8+jmYkvrhSEGmzr8TA6bOjd08P1h88B8C981k6OhMFBcn+B5jobu8fLeMHcOz/H1fbop1FvvYJbGN+FnYIPcv6AfieTWBq63Oy1p/H6FMHoV7xHZ/9r688j2VF7iJ3a5vSced0s9GGACL//gnG7LYDQAFjbAhjzApgKYAVpj4r0BpQAAA3AFjDOeeMsXQAnwB4hHO+KVKLJnounHM4j/wfoHv4NpQkWAvu7bpFtWH95C0xlY6swHnNv8Xk3sW1Kr6tciseBuDawQn+B8QBcs5cr0PCevlaaGWr/IzoGJ7ZB+pl1woyy8plQLPvKqq3FYhBIqtOtlCNnxjRofJp8+E8AGA1gIMA3uac72eMPcUYa/fwvQogizFWDOBBAO3h2A8AGA7gl4yx3W3/ciL+Kogeg35uPfSqHYLMOuz7kGxd+22UVZyBZZVYMVO94jvgOf1jcv/3jovnUGb3s6JfYnw7yBljsI58ACxpkCB3Hvkz9OrdYc+rLvouuNXtC5PqzsO6cpnPvtNzrBjuUf1VNYC/HgycnoeIDEHFFnLOV3HOR3DOh3HOf90me4xzvqLt5xbO+Y2c8+Gc82mc82Nt8l9xzpM455M8/nVcdIPolXBnDRxH/iLIpLRxUPp3TZ0eF5zDtuxPLlMOABhpGXAuuT0mtzc4x/Ji8Zv7DUOjH9YdC5hsh33co4DsETjBNbTsezrsAASemgF14U2CzLL6HbByb38hYwz3jE4SZK8ebkCTRn6faEOB7US3gHMOx6HfA2qNW8gsXVYW2xP5m/VQdm8WZM4b7wESkvyMiCwbzzpxvN5tCrJKwDVxbnLzREoaCNuoB0Wh1oiWb38Jw1EZ1pzOq5bCSM92tZmmwrb8zz773lqQiHSr28d03sGx7IhvMx0ROUj5EN0CrWwV9MqtgswyeCmkpAF+RsSIxnrY/vFHQaQPHwdtVux2Y8uOiGagxYMSkGHrWX+6St85sAz7niDjjgq07H4UXA1co8cn9kQ4b7pHvEfhRsjffO3VNcki4XujxC8Sz++tR4tGYdfRpGe9g4m4xGg8BWeRKWN16ihYBi3tohW5sS3/M6Taalebywoc//5Q1HO4tXPeYWCFKe/Y7SN6hsnNjGXgjVDyFgky3niiVQFpofthtIvmQx8mJmOx/f15nwXn/mN0MmySW9mcaTLwtyPk+4kmpHyILoVrjWjZ9yvA8Dh7LCe0httKXetQl7/dCsvXYuSVuui7MPKHxGwNbxxuRItH8NWgZBkX5/bMJCGMMVhH3Ac5+yJBbtQXoWXPE+B6iHV3JAmOOx8Cl93vI6n2PGxv/smra99EGTfkitkQnt9TT76fKELKh+gyuKHBse/X4I0nBLl1xH2QEmMTReaXxnrYXntGEBm5A+FcdGvMlqAaHK+YIq/uHJkEqRuWy44UjMmwjX0EUsYkQW7U7G19rxiqn5G+MQYOg7r4NkFm2fwFlE2fe/W9PU9FokeevPJmA68eot1PtCDlQ3QJred5XoReXSjIW89+XO5nVIzgHPbXn4FU43Z2cyah5e5HAGvsdh0rSppx2uPMSaLCcOfI2AQ5dCVMtsI+/nFIqWIOP71qBxwH/h84D+0cjnPxbdDzhwoy29+eAztdIsgyrfCKfPvD3gY0qLT7iQakfIiYw7kBZ/ErXocJpdRRsI1+sEsLxAGA5asPoexYL8jURd+FMWx0zNZgcI7n9tQLsluGJ/a4QAN/MCUB9olPQ0oWTZz6uQ1wHvoDOA9BISgWOO79BbjFnZqIOVuQ8KfHgEbxGf9wXDKSPXY/lS0GXtjfEN6LIALSO97JRLeBGyocB/4X2qn3BTmz94V9wuNgctf6M6Rjh2B960VBpg8cHrMzPe18fKIF+8+7fRAMwL1jev6uxxNmSYF90m/AEsQ8xtqZz+EsfgU8hAI8xoChcPybmE1bOnMS9heeFDJfZ9ll3DtWTFn0h70NKGukrAeRhpQPETMMRxVavv0l9PK14gUlCfaJT4FZM7pmYW2w8tOwP/8ImOb2K3B7IloeeALw+NYcbQzO8bvdYkTW9UMSUJDmnRyzp8OsGbBP/i2YrY8g1059APW476wF/tDmXAXVFCKv7P8Gtjeeg2cluR+OS0a23f3R2KRxPLmzNozVE4Eg5UPEBK18PZq3/QeM82LalNYPl99BMqVYiTWsthoJz/5MqE4KAC13/Swm5RI8ebOoyWvX89NJKTFdQ3dCsufAPvm3gCVdkKslb8J54u3gJ2IMjjsf9Aq/tny9CtZlf3QpoDSrhEcnpwp9/nW0GTsrOlfwjhAh5UNEFaOhBC3fPgbH/t8Cmmg7Zwn9Yb/wOcgpw7todW3rqDiDhF//EJIp/Yrz6lugT7skpmupcxp4ulDc9XxnaAJGpfe+XY8nUmI+7JN+AyiiSUw9+hqcx5cFb4Kz2tDy41/ByO4nir/8AHlfvO1SQP82IhFjMsSk/49sqw3J1EcEhpQPERWMlgo4Dj6H5u33Q6/a7nVdSh+PhAufg5SQ2wWr81hH8X4kPP0DL8Wjzrwczhvujvl6flVYh3PNbme6XQYeuzA1wIjeg5wyFPaJT4t54ACox5dBPfpq0IqBp2Wi+aHfwUgVzbw527+E9e2XAM6hSAy/nZYmXN9e4RTKLxCdg5QPEVG41gjn0dfRvPUuaGc+B2CKSmIWWIffDfvk34FZ033OERMMA5ZVy5Hwmx8JGQwAQJs4A467fhazLAbtrC9z4GXTuZ4HxqVgYHIwZbd6B3LaaNgnPOmtgE6+23oOSGv2M1KE9x+Elv96DjxFVDDWVcthfftlgHPM7W/HVaYy5Y9ur0Vpg+/S3ERokPIhIgI3NKilK9C05d+hnvgXYHjbx6W0MUiY+kdYBn6na5OFNtTC/odHYfvXX8B0MYpJvWg+Wn70NOCj8mU0Odes4/4N/7+9c4+Oqrr3+Oc3r2SSQBICgfCSWB4CBSvi83Kvum4rXJYVu3ot3GrFau3SSq291yqP29brrasqYtVrW9eqYrXL1nZda8tCuaK1FrWAtArIQyDyDBJCyIM8JjNzzvndP86BzEwmZNKkM5jsz1qzcmbvfU72/NbM+Z7f3r/928nzTeMG+fn2tMw3ixso+EvP9YbgkqP/7GNvE/nrnThtqXtdpscZXUnk7hVoYbJnGXrlV+StXA62xf0XFBP2d4Ren4grt73VgG222+41RnwMvUJVseo2EHn3VmK7fwJpkkBKwRjypn2f/BkrOq3byDb+7X+h4Lu3ENi8vlNdbO4Col9fmnXhidnKwj/WJy0oFeAns0opDJqfaDr8xVPIP+8BCCZ7Ltp6gMimbxA/9PuM1gI5Y8cTufthtCBZ5IPrXiH/8e9RmWdx78xkcXqrJsYPNyevDzL0HPPNNvzN2M1VtL+/mOjWe9G26k71EiolNOkOwhc+SWDYJbldPNrWQt7K5YQfugtfffKWUlpQRORbPyA2/9asD7XFHeWmN+tZfzTZU/zmp4u4dET/zOHWV/gHTSA889HODzR2O7E9P6X9vbuwm/d2ex1n3EQid68gniJAgc1/Jrz8Lm4ZY/OPI5JD7R/e0sz/7jXzP73BiI+hxzjROqI7VtC+6Zs4jVs6N/DnE6z8CuFLniE4am7uE4RuXk/B0hsJ/unlTnX2pybTdt/PsGfMynq/WuMON7xRz+qDyQkzL6vIM0EGGeILV5B//o/wl1/Wqc5p2kH7ptuJ7nwEJ3r8tNdxKiexZ+E9OEOHJ5X792yj6AeL+PmkVsrDybfL295q4PXqHiY7NZzCiI8hY9RuJ7b3F0TW34xV8xqQOu7tI1Axh/DFTxOqvA5JmRTONr4De8h/+DuEf7QEX0PypmQqQuxf5hNZ+jg6LPsRdx82xpn9Sh1rDiXfvMYPDvDM5aUEfP03eWhfI/588qYuJjTpDvCnbjehWEfWEll/E9E9P0NjDWmvARAtG0HkP3/cKQ+cr+YQYx+6ndXDPiQh8w5xB/7tD8d5aZ/xgP4WTBiNoVtUbayaPxD/6Fk0lv4J0lc6g7wJX8NXdHba+mwix44Q+u1KAutfR9KE3zoVY2n/2j0446dmvW8NUYfHPmjmpztaiKZkbBk3yM+qOUMZkp9bT/GTiIgQHDUXf9kFxHY/gV23MbmBE8U69CLW4dUERs4mOOoqfIVjO11HS4cSWfoY4UeX4d+9teP6kVZmPPdfbP3MlVxcdC0nAq7IxR346psNbKuPs+S8weahoQcY8TF0idrtWEdeI37oJTSSPoJICscSGn8L/iEzc54QNFRfS97K3xF4+1XE7hwOq+IjPncBsWsWZjU7NUBL3OHJHa08vq2ZE7HOgvjpIUF+/dkyRhYa4ekNvvxh5E27F/v4u8SqnkLbDiU3cKJY1auwqlfhK5lOoHwW/rKL8IUThtsKBxH5znLynn2E4NuvJp0+cfNaDoc38N2Rn+epiitoCbjbma/Y2sIbH0d57NISppdlLxXTJxnJ9YrdpqampA7s2bOHCRMm5Ko7ZzTZsI06FnbDZuzadVjH/twpK8EpgsWEzr6BQMWcnM/pyOH9hFY/36WnA2Cfcy7RBd/AqZyU1b5FbeWZXa2s2NLMsfb00VfXjAvzxKwSiv7OkW0D7beljo318Rri+3+JxupP21bCo2ijnMEV5+IrGI2EK/DlDyf0xhpCaULyAdp8IVYNPZ+1pdNYVzKZ/fnDEBEWjC9g0dQipg7pX1kpevv9KS4uTno6NZ7PAEZV0dhxnJb9OM1VOI0fYDdth9PtGOkLEhzzBYJnzUcCOcyy3NZCYMsGAn96mcDO97tsZo8+m9iXvo49/SLIomfWFHP4xe5WntzRSnUXGZGHh33cf2ExX6wM59xr7I+Iz09w9FUEKq50RejAr7sUIY0cJsxh4nuTv0ttBYPx3Tye4IEaArWt+JsVf5NDoFEpiMdYULueBbVu2P7BvDLWlZzDuo8ns3DrZIZXjuHGSUVcOSaf4pCZXk/FiE8/RVXBiaFWC1gtaLwZjdaj0WM4kSOu4LTu79qzSUUCBIZfTrDyenzhEd237wscGznRiDTUIU3HkYbj+GoO4d+3C1/V9rRDa6dOLR9JbN4NWJd+DrLkmTXFHN6vi7H6QDsvVLXRYqX3wkpCwrenD+KWyYUUBMxN6e+N+EMEx8wjMGoudu3bxA+vxmnantnJ8RM4nCA6AqIjkm+XvlYl0OgKUaBRqWis58vH3+H6o+8AUPdeEe8OHs9TxeOJnjWJMRMrmfSpkUwfGiY/YB42MhIfEZkDPAb4gadU9YGU+jzgOeB84DgwX1X3e3VLgJsBG7hDVZMHUQ2AJxZqg1rgxN3tgtUCx3JFxIkTat+FVXs0QVBaUKvFe9/qCozVeqoO7dmWw2kJFhMcOZvA6Hn48sp6dy3HASsO8RgSbUeaG11xaW5EmuqR+mP4Go65YlN/DGmsQ5ye7SJpjxxH/PPXYV10Bfh7/2wVd5SWuNIcd2iOKS1xh8aYUtNmc6TNpqbN5nCrzc5Gq0sP5ySFAeG2qUUsmlpEyQDZFO5MQnxBAiOuIDDiCpzWg1h1G7HrNuI07aBTGqgMcAqFWKGfWPJ2Q/gi6gpTW5RZrdu4rPUDfAcV+QisuJ9qfxm1eeW0FAwlNmgYMmQ4wbJhFA4uoai0lNIhJQwpLiDg79/fkW5/nSLiB34MfA6oBjaJyCpV3ZHQ7GagQVXHi8gC4EFgvohMARYAU4GRwOsiMlF7ug9uBrRvva/zzVaVjnBg7ShKKUuoyKAu5WlW05SdfJ/y/9Wx3D46nsCcFBeNQwZ70w8Fose6bdZrJFSKv+wC/OWXkb9+B4F3t4E+AI6COuA47tyKOl6ZnVBnI/G4JzJxxIp1HJ/GU+kt9sRpHJj2D5Rf9aVuF4re+U4DB1tsbAVLFdsBWxVL3eillrhDS9wVmvY++Kbm+eHGiYX8x7mDKA+bgIIzAV/hWEKFY+Gsa1ErgtO6j5q9Gxha0IZGanDaj6CRo+4DYA9xwoITFro6s5RGSmkEdidXNHuvfUrMgZgDquLqooI6AiqoI265ilt+6gLJ3pSqEA4IklQubjM9+ZeE4eiOv864ifhKziFUeX2PP3+mdBtwICKXAPeq6mzv/RIAVf1hQptXvTbrRSQA1ADDgMWJbRPbnTw3NeDAYDAYDP2P1ICDTPy6UUBivGK1V5a2japaQBNQluG5BoPBYBhgZCI+6WbGUr2Vrtpkcq7BYDAYBhiZzMhWA2MS3o8GUlccnmxT7Q27FQP1mZyb6ooZDAaDof+TieezCZggIpUiEsINIFiV0mYVsNA7/lfgDXUnk1YBC0QkT0QqgQlA520tDQaDwTCg6FZ8vDmcRcCrwE7gN6q6XUTuE5GrvWZPA2UiUgX8Ox2BBtuB3wA7gP8Dbk8X6SYi/y0iW0Vks4isFZGRXrmIyOMiUuXVz+j9R/7kISLLReRDzwYviUhJQt0Szz67RGR2LvuZK0TkWhHZLiKOiMxMqRvw9gF3uYRngyoRWZzr/uQaEVkpIrUisi2hbIiIvCYie7y/pae7Rn9FRMaIyB9FZKf3u/qWV9639lHVnL+AwQnHdwBPesdzgTW4c0cXAxtz3dcc2edKIOAdPwg86B1PAbYAeUAl8BHgz3V/c2CfycAk4E1gZkK5sY9rB7/32c8GQp5NpuS6Xzm2yT8BM4BtCWUPAYu948Unf2cD7QVUADO840G4MeFT+to+Z8QqJlVN3P6ykI6ghHnAc+qyASgRkeznv88xqrpW9dSCgw24c2fg2ucFVY2q6j6gCrgwF33MJaq6U1V3paky9nG5EKhS1b2qGgNewLXNgEVV1+HOSycyD3jWO34WuCarnTpDUNUjqvqed9yMO+I1ij62zxkhPgAicr+IHAKuA77nFZtQ7c7chOsNgrFPdxj7uBg7ZMZwVT0C7g0YKM9xf3KOiIwDzgM20sf2yVpuNxF5HUiXFGyZqv5eVZcBy7xFrIuA7zOAQrW7s4/XZhlgAc+fPC1N+wFrn3SnpSnrl/bpBmMHQ48RkSLgReBOVT3R18lvsyY+qvrZDJv+EngZV3wyCfPuF3RnHxFZCFwF/LN6g64Y+3THgLFPNxg7ZMZREalQ1SPe8H5trjuUK0QkiCs8z6vqb73iPrXPGTHsJiKJm0RcDXzoHa8CbvCi3i4Gmk66fQMJL7HrPcDVqpq4Z68JZT89xj4umSyXMCQvGVkIdOVR92vEdXGeBnaq6iMJVX1qn5xvJgcgIi/iRis5wAHgVlU97BnhCWAO0AZ8VVX/krue5gYvhD0PN2M4wAZVvdWrW4Y7D2Thusdr0l+l/yIiXwD+BzefYCOwWTtyEQ54+wCIyFzgUdzIt5Wqen+Ou5RTRORXwOW4+XqP4o60/A53achY4CBwraqefhe6foiIzALeAj6gI933Utx5nz6zzxkhPgaDwWAYWJwRw24Gg8FgGFgY8TEYDAZD1jHiYzAYDIasY8THYDAYDFnHiI/BYDAYso4RH4PBYDBkHSM+BoPBYMg6RnwMBoPBkHX+H64weD+iR9eaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "n1 = np.random.normal(4, 3, 30000)\n",
    "n2 = np.random.normal(1, 4, 30000)\n",
    "n_diff = n2 - n1\n",
    "sns.distplot(n1, hist=False, label=\"N(2,3)\")\n",
    "sns.distplot(n2, hist=False, label=\"N(1,4)\")\n",
    "sns.distplot(n_diff, hist=False, label=f\"N(4,3) - N(1,4) = N(-1, 5)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we take the distribution of the means of our 2 groups and subtract one from the other, we will have a third distribution. The mean of this final distribution will be the difference in the means and the standard deviation of this distribution will be the square root of the sum of the standard deviations.\n",
    "\n",
    "$\n",
    "\\mu_{diff} = \\mu_1 + \\mu_2\n",
    "$\n",
    "\n",
    "$\n",
    "SE_{diff} = \\sqrt{SE_1 + SE_2} = \\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}\n",
    "$\n",
    "\n",
    "Let's return to our classroom example. We will construct this distribution of the diference. Of course, once we have it, building the 95% CI is very easy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-8.376410208363385, -1.4480327880905248)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "ci = (diff_mu - 1.96*diff_se, diff_mu + 1.96*diff_se)\n",
    "print(ci)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(diff_mu - 4*diff_se, diff_mu + 4*diff_se, 100)\n",
    "y = stats.norm.pdf(x, diff_mu, diff_se)\n",
    "plt.plot(x, y)\n",
    "plt.vlines(ci[1], ymin=0, ymax=.05)\n",
    "plt.vlines(ci[0], ymin=0, ymax=.05, label=\"95% CI\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this at hand, we can say that we are 95% confident that the true difference between the online and face to face group falls between -8.37 and -1.44. We can also construct a **z statistic** by dividing the difference in mean by the \\\\(SE\\\\) of the differences. \n",
    "\n",
    "$\n",
    "z = \\dfrac{\\mu_{diff} - H_{0}}{SE_{diff}} = \\dfrac{(\\mu_1 - \\mu_2) - H_{0}}{\\sqrt{\\sigma_1^2/n_1 + \\sigma_2^2/n_2}}\n",
    "$\n",
    "\n",
    "Where \\\\(H_0\\\\) is the value which we want to test our difference against.\n",
    "\n",
    "The z statistic is a measure of how extreme the observed difference is. To test our hypothesis that the difference in the means is statistically different from zero, we will use contradiction. We will assume that the opposite is true, that is, we will assume that the difference is zero. This is called a null hypothesis, or \\\\(H_0\\\\). Then, we will ask ourselves \"is it likely that we would observe such a difference if the true difference were indeed zero?\" In statistical math terms, we can translate this question to checking how far from zero is our z statistic. \n",
    "\n",
    "Under \\\\(H_0\\\\), the z statistic follows a standard normal distribution. So, if the difference is indeed zero, we would see the z statistic between 2 standard deviation of the mean 95% of the time. The direct consequence of this is that if z falls above or below 2 standard deviations, we can reject the null hypothesis with 95% confidence.\n",
    "\n",
    "Let's see how this looks like in our classroom example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.7792810791031224\n"
     ]
    }
   ],
   "source": [
    "z = diff_mu / diff_se\n",
    "print(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-4,4,100)\n",
    "y = stats.norm.pdf(x, 0, 1)\n",
    "plt.plot(x, y, label=\"Standard Normal\")\n",
    "plt.vlines(z, ymin=0, ymax=.05, label=\"Z statistic\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks like a pretty extreme value. Indeed, it is above 2, which means there is less than a 5% chance that we would see such an extreme value if there were no difference in the groups. This again leads us to conclude that switching from face to face to online classes causes a statistically significant drop in academic performance.\n",
    "\n",
    "One final interesting thing about hypothesis tests is that it is less conservative than checking if the 95% CI from the treated and untreated group overlaps. In other words, if the confidence intervals in the two groups overlap, it can still be the case that the result is statistically significant. For example, let's pretend that the face-to-face group has an average score of 74 and standard error of 7 and the online group has an average score of 71 with a standard error of 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Control 95% CI: (69.04, 72.96)\n",
      "Test 95% CI: (60.28, 87.72)\n",
      "Diff 95% CI: (0.22814141774873375, 5.771858582251266)\n"
     ]
    }
   ],
   "source": [
    "cont_mu, cont_se =  (71, 1)\n",
    "test_mu, test_se = (74, 7)\n",
    "\n",
    "diff_mu = test_mu - cont_mu\n",
    "diff_se = np.sqrt(cont_se + cont_se)\n",
    "\n",
    "print(\"Control 95% CI:\", (cont_mu-1.96*cont_se, cont_mu+1.96*cont_se))\n",
    "print(\"Test 95% CI:\", (test_mu-1.96*test_se, test_mu+1.96*test_se))\n",
    "print(\"Diff 95% CI:\", (diff_mu-1.96*diff_se, diff_mu+1.96*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we construct the confidence intervals for these groups, they overlap. The upper bound for the 95% CI of the online group is 72.96 and the lower bound for the face-to-face group is 60.28. However, once we compute the 95% confidence interval for the difference between the groups, we can see that it does not contain zero. In summary, even though the individual confidence intervals overlap, the difference can still be statistically different from zero.\n",
    "\n",
    "## P-values\n",
    "\n",
    "I've said previously that there is less than 5% chance that we would observe such an extreme value if the difference between online and face to face groups were actually zero. But can we estimate exactly what is that chance? How likely are we to observe such an extreme value? Enters P-Values!\n",
    "\n",
    "Just like with confidence intervals (and most frequentist statistics, as a matter of fact) the true definition of P-values can be very confusing. So, to not take any risks, I'll copy the definition from Wikipedia: \"the p-value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct\". \n",
    "\n",
    "To put it more succinctly, the P-value is the probability of seeing such a data, given that the null-hypothesis is true. It measures how unlikely it is that measurement you are seeing if the null-hypothesis is true. Naturally, this often gets confused with the probability of the null-hypothesis being true. Note the difference here. The P-value is NOT \\\\(P(H_0|data)\\\\), but rather \\\\(P(data|H_0)\\\\).\n",
    "\n",
    "But don't let this complexity fool you. In practical terms, they are pretty straightforward to use.\n",
    "\n",
    "![p_value](./data/img/stats-review/p_value.png)\n",
    "\n",
    "To get the p-value, we need to compute the area under the standard normal distribution before or after the z statistic. Fortunately, we have a computer to do this calculation for us. We can simply plug the z statistic in the CDF of the standard normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-value: 0.0027239680835563383\n"
     ]
    }
   ],
   "source": [
    "print(\"P-value:\", stats.norm.cdf(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that there is only a 0.2% chance of observing this extreme z statistic if the difference was zero. Notice how the P-value is interesting because it avoids us having to specify a confidence level, like 95% or 99%. But, if we wish to report one, from the p-value, we know exactly which confidence will our test pass or fail. For instance, with a p-value of 0.0027, we know that we have significance up to the 0.2% level. So, while the 95% CI for the difference and the 99% CI will neither contain zero, the 99.9% CI will."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI: (-8.376346553082909, -1.4480964433710017)\n",
      "99% CI: (-9.46485353526404, -0.3595894611898709)\n",
      "99.9% CI: (-10.728040658245558, 0.9035976617916459)\n"
     ]
    }
   ],
   "source": [
    "diff_mu = online.mean() - face_to_face.mean()\n",
    "diff_se = np.sqrt(face_to_face.var()/len(face_to_face) + online.var()/len(online))\n",
    "print(\"95% CI:\", (diff_mu - stats.norm.ppf(.975)*diff_se, diff_mu + stats.norm.ppf(.975)*diff_se))\n",
    "print(\"99% CI:\", (diff_mu - stats.norm.ppf(.995)*diff_se, diff_mu + stats.norm.ppf(.995)*diff_se))\n",
    "print(\"99.9% CI:\", (diff_mu - stats.norm.ppf(.9995)*diff_se, diff_mu + stats.norm.ppf(.9995)*diff_se))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Keys Ideas\n",
    "\n",
    "We've seen how important it is to know the Moivre’s equation and we used it to place a degree of certainty around our estimates. Namely, we figured out that the online classes cause a decrease in academic performance compared to face to face classes. We also saw that this was a statistically significant result. We did it by comparing the Confidence Intervals of the means for the 2 groups, by looking at the confidence interval for the difference, by doing a hypothesis test and by looking at the p-value. Let's wrap everything up in a single function that does A/B testing comparison like the one we did above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.54748458333333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226955 +- 3.4641250548559537\n",
      "Z Statistic -2.7792810791031224\n",
      "P-Value 0.0027239680835563383\n"
     ]
    }
   ],
   "source": [
    "def AB_test(test: pd.Series, control: pd.Series, confidence=0.95, h0=0):\n",
    "    mu1, mu2 = test.mean(), control.mean()\n",
    "    se1, se2 = test.std() / np.sqrt(len(test)), control.std() / np.sqrt(len(control))\n",
    "    \n",
    "    diff = mu1 - mu2\n",
    "    se_diff = np.sqrt(test.var()/len(test) + control.var()/len(control))\n",
    "    \n",
    "    z_stats = (diff-h0)/se_diff\n",
    "    p_value = stats.norm.cdf(z_stats)\n",
    "    \n",
    "    def critial(se): return -se*stats.norm.ppf((1 - confidence)/2)\n",
    "    \n",
    "    print(f\"Test {confidence*100}% CI: {mu1} +- {critial(se1)}\")\n",
    "    print(f\"Control {confidence*100}% CI: {mu2} +- {critial(se2)}\")\n",
    "    print(f\"Test-Control {confidence*100}% CI: {diff} +- {critial(se_diff)}\")\n",
    "    print(f\"Z Statistic {z_stats}\")\n",
    "    print(f\"P-Value {p_value}\")\n",
    "        \n",
    "AB_test(online, face_to_face)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our function is generic enough, we can test other null hypotheses. For instance, can we try to reject that the difference between online and face to face class performance is -1. With the results we get, we can say with 95% confidence that the difference is greater than -1. But we can't say it with 99% confidence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test 95.0% CI: 73.63526308510637 +- 3.0127770572134565\n",
      "Control 95.0% CI: 78.54748458333333 +- 1.7097768273108005\n",
      "Test-Control 95.0% CI: -4.912221498226955 +- 3.4641250548559537\n",
      "Z Statistic -2.2134920404560883\n",
      "P-Value 0.013431870694630114\n"
     ]
    }
   ],
   "source": [
    "AB_test(online, face_to_face, h0=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "I like to think of this entire book as a tribute to Joshua Angrist, Alberto Abadie and Christopher Walters for their amazing Econometrics class. Most of the ideas here are taken from their classes at the American Economic Association. Watching them is what is keeping me sane during this tough year of 2020.\n",
    "* [Cross-Section Econometrics](https://www.aeaweb.org/conference/cont-ed/2017-webcasts)\n",
    "* [Mastering Mostly Harmless Econometrics](https://www.aeaweb.org/conference/cont-ed/2020-webcasts)\n",
    "\n",
    "I'll also like to reference the amazing books from Angrist. They have shown me that Econometrics, or 'Metrics as they call it, is not only extremely useful but also profoundly fun.\n",
    "\n",
    "* [Mostly Harmless Econometrics](https://www.mostlyharmlesseconometrics.com/)\n",
    "* [Mastering 'Metrics](https://www.masteringmetrics.com/)\n",
    "\n",
    "My final reference is Miguel Hernan and Jamie Robins' book. It has been my trustworthy companion in the most thorny causal questions I had to answer.\n",
    "\n",
    "* [Causal Inference Book](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/)\n",
    "\n",
    "In this particular section, I've also referenced The [Most Dangerous Equation](https://www.researchgate.net/publication/255612702_The_Most_Dangerous_Equation), by Howard Wainer.\n",
    "\n",
    "Finally, if you are curious about the correct interpretation of the statistical concepts we've discussed here, I recommend reading the paper by Greenland et al, 2016: [Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations](https://link.springer.com/content/pdf/10.1007/s10654-016-0149-3.pdf).\n",
    "\n",
    "![img](./data/img/poetry.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
